File Coverage

blib/lib/Math/AnyNum.pm

Criterion	Covered	Total	%
statement	12	14	85.7
branch			n/a
condition			n/a
subroutine	5	5	100.0
pod			n/a
total	17	19	89.4

line	stmt	sub	time	code
1				package Math::AnyNum;
2
3	1	1	50475	use 5.014;
	1		4
4	1	1	4	use strict;
	1		2
	1		16
5	1	1	4	use warnings;
	1		1
	1		40
6
7	1	1	4	no warnings qw(numeric uninitialized);
	1		2
	1		26
8
9	1	1	118	use Math::MPFR qw();
	0
	0
10				use Math::GMPq qw();
11				use Math::GMPz qw();
12				use Math::MPC qw();
13
14				use POSIX qw(ULONG_MAX LONG_MIN);
15
16				our $VERSION = '0.17';
17				our ($ROUND, $PREC);
18
19				BEGIN {
20				$ROUND = Math::MPFR::MPFR_RNDN();
21				$PREC = 192;
22				}
23
24				use overload
25				'""' => \&stringify,
26				'0+' => \&numify,
27				bool => \&boolify,
28
29				'+' => \&add,
30				'*' => \&mul,
31
32				'==' => \&eq,
33				'!=' => \&ne,
34
35				'&' => \&and,
36				'\|' => \&or,
37				'^' => \&xor,
38				'~' => \¬,
39
40				'>' => sub { $_[2] ? (goto <) : (goto >) },
41				'>=' => sub { $_[2] ? (goto &le) : (goto &ge) },
42				'<' => sub { $_[2] ? (goto >) : (goto <) },
43				'<=' => sub { $_[2] ? (goto &ge) : (goto &le) },
44
45				'<=>' => sub { $_[2] ? -(&cmp($_[0], $_[1]) // return undef) : &cmp($_[0], $_[1]) },
46
47				'>>' => sub { @_ = ($_[1], $_[0]) if $_[2]; goto &rsft },
48				'<<' => sub { @_ = ($_[1], $_[0]) if $_[2]; goto &lsft },
49				'/' => sub { @_ = ($_[1], $_[0]) if $_[2]; goto &div },
50				'-' => sub { @_ = ($_[1], $_[0]) if $_[2]; goto &sub },
51
52				'**' => sub { @_ = $_[2] ? @_[1, 0] : @_[0, 1]; goto &pow },
53				'%' => sub { @_ = $_[2] ? @_[1, 0] : @_[0, 1]; goto &mod },
54
55				atan2 => sub { @_ = $_[2] ? @_[1, 0] : @_[0, 1]; goto &atan2 },
56
57				eq => sub { "$_[0]" eq "$_[1]" },
58				ne => sub { "$_[0]" ne "$_[1]" },
59
60				cmp => sub { $_[2] ? ("$_[1]" cmp $_[0]->stringify) : ($_[0]->stringify cmp "$_[1]") },
61
62				neg => \&neg,
63				sin => \&sin,
64				cos => \&cos,
65				exp => \&exp,
66				log => \&ln,
67				int => \&int,
68				abs => \&abs,
69				sqrt => \&sqrt;
70
71				{
72
73				my %const = ( # prototypes are assigned in import()
74				e => \&e,
75				phi => \&phi,
76				tau => \&tau,
77				pi => \&pi,
78				ln2 => \&ln2,
79				euler => \&euler,
80				i => \&i,
81				catalan => \&catalan,
82				Inf => \&inf,
83				NaN => \&nan,
84				);
85
86				my %trig = (
87				sin => sub (_) { goto &sin }, # built-in function
88				sinh => \&sinh,
89				asin => \&asin,
90				asinh => \&asinh,
91
92				cos => sub (_) { goto &cos }, # built-in function
93				cosh => \&cosh,
94				acos => \&acos,
95				acosh => \&acosh,
96
97				tan => \&tan,
98				tanh => \&tanh,
99				atan => \&atan,
100				atanh => \&atanh,
101
102				cot => \&cot,
103				coth => \&coth,
104				acot => \&acot,
105				acoth => \&acoth,
106
107				sec => \&sec,
108				sech => \&sech,
109				asec => \&asec,
110				asech => \&asech,
111
112				csc => \&csc,
113				csch => \&csch,
114				acsc => \&acsc,
115				acsch => \&acsch,
116
117				atan2 => \&atan2,
118				deg2rad => \°2rad,
119				rad2deg => \&rad2deg,
120				);
121
122				my %special = (
123				beta => \&beta,
124				zeta => \&zeta,
125				eta => \&eta,
126
127				gamma => \&gamma,
128				lgamma => \&lgamma,
129				lngamma => \&lngamma,
130				digamma => \&digamma,
131
132				Ai => \&Ai,
133				Ei => \&Ei,
134				Li => \&Li,
135				Li2 => \&Li2,
136
137				lgrt => \&lgrt,
138				LambertW => \&LambertW,
139
140				BesselJ => \&BesselJ,
141				BesselY => \&BesselY,
142
143				pow => \&pow,
144				sqr => \&sqr,
145				norm => \&norm,
146				sqrt => sub (_) { goto &sqrt }, # built-in function
147				cbrt => \&cbrt,
148				root => \&root,
149
150				exp => sub (_) { goto &exp }, # built-in function
151				exp2 => \&exp2,
152				exp10 => \&exp10,
153
154				ln => sub ($) { goto &ln }, # used in overloading
155				log => \&log, # built-in function
156				log2 => \&log2,
157				log10 => \&log10,
158
159				mod => \&mod,
160				abs => sub (_) { goto &abs }, # built-in function
161
162				erf => \&erf,
163				erfc => \&erfc,
164
165				hypot => \&hypot,
166				agm => \&agm,
167
168				bernreal => \&bernreal,
169				harmreal => \&harmreal,
170
171				polygonal_root => \&polygonal_root,
172				polygonal_root2 => \&polygonal_root2,
173				);
174
175				my %ntheory = (
176				factorial => \&factorial,
177				dfactorial => \&dfactorial,
178				mfactorial => \&mfactorial,
179				primorial => \&primorial,
180				binomial => \&binomial,
181
182				rising_factorial => \&rising_factorial,
183				falling_factorial => \&falling_factorial,
184
185				lucas => \&lucas,
186				fibonacci => \&fibonacci,
187
188				faulhaber_sum => \&faulhaber_sum,
189
190				bernfrac => \&bernfrac,
191				harmfrac => \&harmfrac,
192
193				lcm => \&lcm,
194				gcd => \&gcd,
195				valuation => \&valuation,
196				kronecker => \&kronecker,
197
198				remdiv => \&remdiv,
199				divmod => \&divmod,
200
201				iadd => \&iadd,
202				isub => \&isub,
203				imul => \&imul,
204				idiv => \&idiv,
205				imod => \&imod,
206
207				ipow => \&ipow,
208				ipow2 => \&ipow2,
209				ipow10 => \&ipow10,
210
211				iroot => \&iroot,
212				isqrt => \&isqrt,
213				icbrt => \&icbrt,
214
215				ilog => \&ilog,
216				ilog2 => \&ilog2,
217				ilog10 => \&ilog10,
218
219				isqrtrem => \&isqrtrem,
220				irootrem => \&irootrem,
221
222				polygonal => \&polygonal,
223				ipolygonal_root => \&ipolygonal_root,
224				ipolygonal_root2 => \&ipolygonal_root2,
225
226				powmod => \&powmod,
227				invmod => \&invmod,
228
229				is_power => \&is_power,
230				is_square => \&is_square,
231				is_polygonal => \&is_polygonal,
232				is_polygonal2 => \&is_polygonal2,
233
234				is_prime => \&is_prime,
235				is_coprime => \&is_coprime,
236				next_prime => \&next_prime,
237				);
238
239				my %misc = (
240				rand => \&rand,
241				irand => \&irand,
242
243				seed => \&seed,
244				iseed => \&iseed,
245
246				floor => \&floor,
247				ceil => \&ceil,
248				round => \&round,
249				sgn => \&sgn,
250				acmp => \&acmp,
251
252				popcount => \&popcount,
253
254				neg => sub ($) { goto &neg }, # used in overloading
255				inv => \&inv,
256				conj => \&conj,
257				real => \&real,
258				imag => \&imag,
259				reals => \&reals,
260
261				int => sub (_) { goto &int }, # built-in function
262				rat => \&rat,
263				float => \&float,
264				complex => \&complex,
265
266				numerator => \&numerator,
267				denominator => \&denominator,
268				nude => \&nude,
269
270				digits => \&digits,
271
272				as_bin => \&as_bin,
273				as_hex => \&as_hex,
274				as_oct => \&as_oct,
275				as_int => \&as_int,
276				as_frac => \&as_frac,
277				as_dec => \&as_dec,
278
279				rat_approx => \&rat_approx,
280
281				is_inf => \&is_inf,
282				is_ninf => \&is_ninf,
283				is_neg => \&is_neg,
284				is_pos => \&is_pos,
285				is_nan => \&is_nan,
286				is_rat => \&is_rat,
287				is_real => \&is_real,
288				is_imag => \&is_imag,
289				is_int => \&is_int,
290				is_complex => \&is_complex,
291				is_zero => \&is_zero,
292				is_one => \&is_one,
293				is_mone => \&is_mone,
294
295				is_odd => \&is_odd,
296				is_even => \&is_even,
297				is_div => \&is_div,
298				);
299
300				sub import {
301				shift;
302
303				my $caller = caller(0);
304
305				while (@_) {
306				my $name = shift(@_);
307
308				if ($name eq ':overload') {
309				overload::constant
310				integer => sub { bless \Math::GMPz::Rmpz_init_set_ui($_[0]) },
311				float => sub { bless \_str2obj($_[0]) },
312				binary => sub {
313				my $const = ($_[0] =~ tr/_//dr);
314				my $prefix = substr($const, 0, 2);
315				bless \(
316				$prefix eq '0x' ? Math::GMPz::Rmpz_init_set_str(substr($const, 2) \|\| 0, 16)
317				: $prefix eq '0b' ? Math::GMPz::Rmpz_init_set_str(substr($const, 2) \|\| 0, 2)
318				: Math::GMPz::Rmpz_init_set_str(substr($const, 1) \|\| 0, 8)
319				);
320				};
321
322				# Export 'Inf', 'NaN' and 'i' as constants
323				foreach my $pair (['Inf', inf()], ['NaN', nan()], ['i', i()]) {
324				my $sub = $caller . '::' . $pair->[0];
325				no strict 'refs';
326				no warnings 'redefine';
327				my $value = $pair->[1];
328				*$sub = sub () { $value };
329				}
330				}
331				elsif (exists $const{$name}) {
332				no strict 'refs';
333				no warnings 'redefine';
334				my $caller_sub = $caller . '::' . $name;
335				my $sub = $const{$name};
336				my $value = $sub->();
337				*$caller_sub = sub() { $value }
338				}
339				elsif ( exists($special{$name})
340				or exists($trig{$name})
341				or exists($ntheory{$name})
342				or exists($misc{$name})) {
343				no strict 'refs';
344				no warnings 'redefine';
345				my $caller_sub = $caller . '::' . $name;
346				*$caller_sub = $ntheory{$name} // $special{$name} // $trig{$name} // $misc{$name};
347				}
348				elsif ($name eq ':trig') {
349				push @_, keys(%trig);
350				}
351				elsif ($name eq ':ntheory') {
352				push @_, keys(%ntheory);
353				}
354				elsif ($name eq ':special') {
355				push @_, keys(%special);
356				}
357				elsif ($name eq ':misc') {
358				push @_, keys(%misc);
359				}
360				elsif ($name eq ':all') {
361				push @_, keys(%const), keys(%trig), keys(%special), keys(%ntheory), keys(%misc);
362				}
363				elsif ($name eq 'PREC') {
364				my $prec = CORE::int(shift(@_));
365				if ( $prec < Math::MPFR::RMPFR_PREC_MIN()
366				or $prec > Math::MPFR::RMPFR_PREC_MAX()) {
367				die "invalid value for <>: must be between "
368				. Math::MPFR::RMPFR_PREC_MIN() . " and "
369				. Math::MPFR::RMPFR_PREC_MAX()
370				. ", but got <<$prec>>";
371				}
372				$PREC = $prec;
373				}
374				else {
375				die "unknown import: <<$name>>";
376				}
377				}
378				return;
379				}
380
381				sub unimport {
382				overload::remove_constant('binary', '', 'float', '', 'integer');
383				}
384				}
385
386				# Converts a string into an mpq object
387				sub _str2obj {
388				my ($s) = @_;
389
390				$s \|\| goto &_zero;
391
392				$s = lc($s);
393
394				if ($s eq 'inf' or $s eq '+inf') {
395				goto &_inf;
396				}
397				elsif ($s eq '-inf') {
398				goto &_ninf;
399				}
400				elsif ($s eq 'nan') {
401				goto &_nan;
402				}
403
404				# Remove underscores
405				$s =~ tr/_//d;
406
407				# Performance improvement for Perl integers
408				if (CORE::int($s) eq $s and $s > LONG_MIN and $s < ULONG_MAX) {
409				return (
410				$s < 0
411				? Math::GMPz::Rmpz_init_set_si($s)
412				: Math::GMPz::Rmpz_init_set_ui($s)
413				);
414				}
415
416				# Complex number
417				if (substr($s, -1) eq 'i') {
418
419				if ($s eq 'i' or $s eq '+i') {
420				my $r = Math::MPC::Rmpc_init2($PREC);
421				Math::MPC::Rmpc_set_ui_ui($r, 0, 1, $ROUND);
422				return $r;
423				}
424				elsif ($s eq '-i') {
425				my $r = Math::MPC::Rmpc_init2($PREC);
426				Math::MPC::Rmpc_set_si_si($r, 0, -1, $ROUND);
427				return $r;
428				}
429
430				my ($re, $im);
431
432				state $numeric_re = qr/[+-]?+(?=\.?[0-9])[0-9]*+(?:\.[0-9]++)?(?:[Ee](?:[+-]?+[0-9]+))?/;
433				state $unsigned_re = qr/(?=\.?[0-9])[0-9]*+(?:\.[0-9]++)?(?:[Ee](?:[+-]?+[0-9]+))?/;
434
435				if ($s =~ /^($numeric_re)\s([-+])\s($unsigned_re)i\z/o) {
436				($re, $im) = ($1, $3);
437				$im = "-$im" if $2 eq '-';
438				}
439				elsif ($s =~ /^($numeric_re)i\z/o) {
440				($re, $im) = (0, $1);
441				}
442				elsif ($s =~ /^($numeric_re)\s([-+])\si\z/o) {
443				($re, $im) = ($1, 1);
444				$im = -1 if $2 eq '-';
445				}
446
447				if (defined($re) and defined($im)) {
448
449				my $r = Math::MPC::Rmpc_init2($PREC);
450
451				$re = _str2obj($re);
452				$im = _str2obj($im);
453
454				my $sig = join(' ', ref($re), ref($im));
455
456				if ($sig eq q{Math::MPFR Math::MPFR}) {
457				Math::MPC::Rmpc_set_fr_fr($r, $re, $im, $ROUND);
458				}
459				elsif ($sig eq q{Math::GMPz Math::GMPz}) {
460				Math::MPC::Rmpc_set_z_z($r, $re, $im, $ROUND);
461				}
462				elsif ($sig eq q{Math::GMPz Math::MPFR}) {
463				Math::MPC::Rmpc_set_z_fr($r, $re, $im, $ROUND);
464				}
465				elsif ($sig eq q{Math::MPFR Math::GMPz}) {
466				Math::MPC::Rmpc_set_fr_z($r, $re, $im, $ROUND);
467				}
468				else { # this should never happen
469				$re = _any2mpfr($re);
470				$im = _any2mpfr($im);
471				Math::MPC::Rmpc_set_fr_fr($r, $re, $im, $ROUND);
472				}
473
474				return $r;
475				}
476				}
477
478				# Floating point value
479				if ($s =~ tr/e.//) {
480				my $r = Math::MPFR::Rmpfr_init2($PREC);
481				if (Math::MPFR::Rmpfr_set_str($r, $s, 10, $ROUND)) {
482				Math::MPFR::Rmpfr_set_nan($r);
483				}
484				return $r;
485				}
486
487				# Fractional value
488				if (index($s, '/') != -1 and $s =~ m{^\s[-+]?[0-9]+\s/\s[-+]?[1-9]+[0-9]\s*\z}) {
489				my $r = Math::GMPq::Rmpq_init();
490				Math::GMPq::Rmpq_set_str($r, $s, 10);
491				Math::GMPq::Rmpq_canonicalize($r);
492				return $r;
493				}
494
495				$s =~ s/^\+//;
496
497				eval { Math::GMPz::Rmpz_init_set_str($s, 10) } // goto &_nan;
498				}
499
500				# Parse a base-10 string as a base-10 fraction
501				sub _str2frac {
502				my ($str) = @_;
503
504				my $sign = substr($str, 0, 1);
505				if ($sign eq '-') {
506				substr($str, 0, 1, '');
507				$sign = '-';
508				}
509				else {
510				substr($str, 0, 1, '') if ($sign eq '+');
511				$sign = '';
512				}
513
514				my $i;
515				if (($i = index($str, 'e')) != -1) {
516
517				my $exp = substr($str, $i + 1);
518
519				# Handle specially numbers with very big exponents
520				# (not a very good solution, but this will happen very rarely, if ever)
521				if (CORE::abs($exp) >= 1000000) {
522				Math::MPFR::Rmpfr_set_str((my $mpfr = Math::MPFR::Rmpfr_init2($PREC)), "$sign$str", 10, $ROUND);
523				Math::MPFR::Rmpfr_get_q((my $mpq = Math::GMPq::Rmpq_init()), $mpfr);
524				return Math::GMPq::Rmpq_get_str($mpq, 10);
525				}
526
527				my ($before, $after) = split(/\./, substr($str, 0, $i));
528
529				if (!defined($after)) { # return faster for numbers like "13e2"
530				if ($exp >= 0) {
531				return ("$sign$before" . ('0' x $exp));
532				}
533				else {
534				$after = '';
535				}
536				}
537
538				my $numerator = "$before$after";
539				my $denominator = "1";
540
541				if ($exp < 1) {
542				$denominator .= '0' x (CORE::abs($exp) + CORE::length($after));
543				}
544				else {
545				my $diff = ($exp - CORE::length($after));
546				if ($diff >= 0) {
547				$numerator .= '0' x $diff;
548				}
549				else {
550				my $s = "$before$after";
551				substr($s, $exp + CORE::length($before), 0, '.');
552				return _str2frac("$sign$s");
553				}
554				}
555
556				"$sign$numerator/$denominator";
557				}
558				elsif (($i = index($str, '.')) != -1) {
559				my ($before, $after) = (substr($str, 0, $i), substr($str, $i + 1));
560				if (($after =~ tr/0//) == CORE::length($after)) {
561				return "$sign$before";
562				}
563				$sign . ("$before$after/1" =~ s/^0+//r) . ('0' x CORE::length($after));
564				}
565				else {
566				"$sign$str";
567				}
568				}
569
570				#
571				## MPZ
572				#
573				sub _mpz2mpq {
574				my $r = Math::GMPq::Rmpq_init();
575				Math::GMPq::Rmpq_set_z($r, $_[0]);
576				$r;
577				}
578
579				sub _mpz2mpfr {
580				my $r = Math::MPFR::Rmpfr_init2($PREC);
581				Math::MPFR::Rmpfr_set_z($r, $_[0], $ROUND);
582				$r;
583				}
584
585				sub _mpz2mpc {
586				my $r = Math::MPC::Rmpc_init2($PREC);
587				Math::MPC::Rmpc_set_z($r, $_[0], $ROUND);
588				$r;
589				}
590
591				#
592				## MPQ
593				#
594
595				sub _mpq2mpz {
596				my $z = Math::GMPz::Rmpz_init();
597				Math::GMPz::Rmpz_set_q($z, $_[0]);
598				$z;
599				}
600
601				sub _mpq2mpfr {
602				my $r = Math::MPFR::Rmpfr_init2($PREC);
603				Math::MPFR::Rmpfr_set_q($r, $_[0], $ROUND);
604				$r;
605				}
606
607				sub _mpq2mpc {
608				my $r = Math::MPC::Rmpc_init2($PREC);
609				Math::MPC::Rmpc_set_q($r, $_[0], $ROUND);
610				$r;
611				}
612
613				#
614				## MPFR
615				#
616
617				sub _mpfr2mpc {
618				my $r = Math::MPC::Rmpc_init2($PREC);
619				Math::MPC::Rmpc_set_fr($r, $_[0], $ROUND);
620				$r;
621				}
622
623				#
624				## Any
625				#
626
627				sub _any2mpc {
628				my ($x) = @_;
629
630				ref($x) eq 'Math::MPC' && return $x;
631				ref($x) eq 'Math::GMPq' && goto &_mpq2mpc;
632				ref($x) eq 'Math::GMPz' && goto &_mpz2mpc;
633
634				goto &_mpfr2mpc;
635				}
636
637				sub _any2mpfr {
638				my ($x) = @_;
639
640				ref($x) eq 'Math::MPFR' && return $x;
641				ref($x) eq 'Math::GMPq' && goto &_mpq2mpfr;
642				ref($x) eq 'Math::GMPz' && goto &_mpz2mpfr;
643
644				my $fr = Math::MPFR::Rmpfr_init2($PREC);
645				Math::MPC::RMPC_IM($fr, $x);
646
647				Math::MPFR::Rmpfr_zero_p($fr)
648				? Math::MPC::RMPC_RE($fr, $x)
649				: Math::MPFR::Rmpfr_set_nan($fr);
650
651				$fr;
652				}
653
654				sub _any2mpz {
655				my ($x) = @_;
656
657				ref($x) eq 'Math::GMPz' && return $x;
658				ref($x) eq 'Math::GMPq' && goto &_mpq2mpz;
659
660				if (ref($x) eq 'Math::MPFR') {
661				if (Math::MPFR::Rmpfr_number_p($x)) {
662				my $z = Math::GMPz::Rmpz_init();
663				Math::MPFR::Rmpfr_get_z($z, $x, Math::MPFR::MPFR_RNDZ);
664				return $z;
665				}
666				return;
667				}
668
669				(@_) = _any2mpfr($x);
670				goto &_any2mpz;
671				}
672
673				sub _any2mpq {
674				my ($x) = @_;
675
676				ref($x) eq 'Math::GMPq' && return $x;
677				ref($x) eq 'Math::GMPz' && goto &_mpz2mpq;
678
679				if (ref($x) eq 'Math::MPFR') {
680				if (Math::MPFR::Rmpfr_number_p($x)) {
681				my $q = Math::GMPq::Rmpq_init();
682				Math::MPFR::Rmpfr_get_q($q, $x);
683				return $q;
684				}
685				return;
686				}
687
688				(@_) = _any2mpfr($x);
689				goto &_any2mpq;
690				}
691
692				sub _any2ui {
693				my ($x) = @_;
694				goto(ref($x) =~ tr/:/_/rs);
695
696				Math_GMPz: {
697
698				if (Math::GMPz::Rmpz_fits_ulong_p($x)) {
699				goto &Math::GMPz::Rmpz_get_ui;
700				}
701
702				return;
703				}
704
705				Math_GMPq: {
706
707				if (Math::GMPq::Rmpq_integer_p($x)) {
708				@_ = ($x = _mpq2mpz($x));
709				goto Math_GMPz;
710				}
711
712				my $d = CORE::int(Math::GMPq::Rmpq_get_d($x));
713				return (($d < 0 or $d > ULONG_MAX) ? undef : $d);
714				}
715
716				Math_MPFR: {
717
718				if (Math::MPFR::Rmpfr_integer_p($x) and Math::MPFR::Rmpfr_fits_ulong_p($x, $ROUND)) {
719				push @_, $ROUND;
720				goto &Math::MPFR::Rmpfr_get_ui;
721				}
722
723				if (Math::MPFR::Rmpfr_number_p($x)) {
724				my $d = CORE::int(Math::MPFR::Rmpfr_get_d($x, $ROUND));
725				return (($d < 0 or $d > ULONG_MAX) ? undef : $d);
726				}
727
728				return;
729				}
730
731				Math_MPC: {
732				@_ = ($x = _any2mpfr($x));
733				goto Math_MPFR;
734				}
735				}
736
737				sub _any2si {
738				my ($x) = @_;
739				goto(ref($x) =~ tr/:/_/rs);
740
741				Math_GMPz: {
742
743				if (Math::GMPz::Rmpz_fits_slong_p($x)) {
744				goto &Math::GMPz::Rmpz_get_si;
745				}
746
747				if (Math::GMPz::Rmpz_fits_ulong_p($x)) {
748				goto &Math::GMPz::Rmpz_get_ui;
749				}
750
751				return;
752				}
753
754				Math_GMPq: {
755
756				if (Math::GMPq::Rmpq_integer_p($x)) {
757				@_ = ($x = _mpq2mpz($x));
758				goto Math_GMPz;
759				}
760
761				my $d = CORE::int(Math::GMPq::Rmpq_get_d($x));
762				return (($d < LONG_MIN or $d > ULONG_MAX) ? undef : $d);
763				}
764
765				Math_MPFR: {
766
767				if (Math::MPFR::Rmpfr_integer_p($x)) {
768				if (Math::MPFR::Rmpfr_fits_slong_p($x, $ROUND)) {
769				push @_, $ROUND;
770				goto &Math::MPFR::Rmpfr_get_si;
771				}
772
773				if (Math::MPFR::Rmpfr_fits_ulong_p($x, $ROUND)) {
774				push @_, $ROUND;
775				goto &Math::MPFR::Rmpfr_get_ui;
776				}
777				}
778
779				if (Math::MPFR::Rmpfr_number_p($x)) {
780				my $d = CORE::int(Math::MPFR::Rmpfr_get_d($x, $ROUND));
781				return (($d < LONG_MIN or $d > ULONG_MAX) ? undef : $d);
782				}
783
784				return;
785				}
786
787				Math_MPC: {
788				@_ = ($x = _any2mpfr($x));
789				goto Math_MPFR;
790				}
791				}
792
793				#
794				## Anything to MPFR (including strings)
795				#
796				sub _star2mpfr {
797				my ($x) = @_;
798
799				$x =
800				ref($x) eq __PACKAGE__ ? $$x
801				: ref($x) ? _star2obj($x)
802				: _str2obj($x);
803
804				ref($x) eq 'Math::MPFR' and return $x;
805
806				(@_) = $x;
807				ref($x) eq 'Math::GMPz' && goto &_mpz2mpfr;
808				ref($x) eq 'Math::GMPq' && goto &_mpq2mpfr;
809				goto &_any2mpfr;
810				}
811
812				#
813				## Anything to GMPz (including strings)
814				#
815				sub _star2mpz {
816				my ($x) = @_;
817
818				$x =
819				ref($x) eq __PACKAGE__ ? $$x
820				: ref($x) ? _star2obj($x)
821				: _str2obj($x);
822
823				ref($x) eq 'Math::GMPz' and return $x;
824
825				(@_) = $x;
826				ref($x) eq 'Math::GMPq' and goto &_mpq2mpz;
827				goto &_any2mpz;
828				}
829
830				#
831				## Anything to MPFR or MPC, in this order (including strings)
832				#
833				sub _star2mpfr_mpc {
834				my ($x) = @_;
835
836				$x =
837				ref($x) eq __PACKAGE__ ? $$x
838				: ref($x) ? _star2obj($x)
839				: _str2obj($x);
840
841				if ( ref($x) eq 'Math::MPFR'
842				or ref($x) eq 'Math::MPC') {
843				return $x;
844				}
845
846				(@_) = $x;
847				ref($x) eq 'Math::GMPz' && goto &_mpz2mpfr;
848				ref($x) eq 'Math::GMPq' && goto &_mpq2mpfr;
849				goto &_any2mpfr; # this should not happen
850				}
851
852				# Anything to a {GMP*, MPFR or MPC} object
853				sub _star2obj {
854				my ($x) = @_;
855
856				ref($x) \|\| goto &_str2obj;
857
858				if (ref($x) eq __PACKAGE__) {
859				$$x;
860				}
861				elsif ( ref($x) eq 'Math::GMPz'
862				or ref($x) eq 'Math::GMPq'
863				or ref($x) eq 'Math::MPFR'
864				or ref($x) eq 'Math::MPC') {
865				$x;
866				}
867				else {
868				(@_) = "$x";
869				goto &_str2obj;
870				}
871				}
872
873				sub new {
874				my ($class, $num, $base) = @_;
875
876				my $ref = ref($num);
877
878				# Special string values
879				if (!$ref and (!defined($base) or CORE::int($base) == 10)) {
880				return bless \_str2obj($num), $class;
881				}
882
883				# Special case
884				if (!defined($base) and $ref eq __PACKAGE__) {
885				return $num;
886				}
887
888				# Number with base
889				if (defined($base) and CORE::int($base) != 10) {
890
891				my $int_base = CORE::int($base);
892
893				if ($int_base < 2 or $int_base > 36) {
894				require Carp;
895				Carp::croak("base must be between 2 and 36, got $base");
896				}
897
898				$num = defined($num) ? "$num" : '0';
899
900				if (index($num, '/') != -1) {
901				my $r = Math::GMPq::Rmpq_init();
902				eval { Math::GMPq::Rmpq_set_str($r, $num, $int_base); 1 } // goto &nan;
903
904				if (Math::GMPq::Rmpq_get_str($r, 10) !~ m{^\s[-+]?[0-9]+\s/\s[-+]?[1-9]+[0-9]\s*\z}) {
905				goto &nan;
906				}
907
908				Math::GMPq::Rmpq_canonicalize($r);
909				return bless \$r, $class;
910				}
911				elsif (index($num, '.') != -1) {
912				my $r = Math::MPFR::Rmpfr_init2($PREC);
913				if (Math::MPFR::Rmpfr_set_str($r, $num, $int_base, $ROUND)) {
914				Math::MPFR::Rmpfr_set_nan($r);
915				}
916				return bless \$r, $class;
917				}
918				else {
919				return bless \(eval { Math::GMPz::Rmpz_init_set_str($num, $int_base) } // goto &nan), $class;
920				}
921				}
922
923				bless \_star2obj($num), $class;
924				}
925
926				sub new_si {
927				my ($class, $si) = @_;
928				bless \Math::GMPz::Rmpz_init_set_si($si), $class;
929				}
930
931				sub new_ui {
932				my ($class, $ui) = @_;
933				bless \Math::GMPz::Rmpz_init_set_ui($ui), $class;
934				}
935
936				sub new_z {
937				my ($class, $str, $base) = @_;
938				bless \Math::GMPz::Rmpz_init_set_str($str, $base // 10), $class;
939				}
940
941				sub new_q {
942				my ($class, $num, $den, $base) = @_;
943				my $r = Math::GMPq::Rmpq_init();
944
945				if (defined($den)) {
946				Math::GMPq::Rmpq_set_str($r, "$num/$den", $base // 10);
947				}
948				else {
949				Math::GMPq::Rmpq_set_str($r, "$num", $base // 10);
950				}
951
952				Math::GMPq::Rmpq_canonicalize($r);
953				bless \$r, $class;
954				}
955
956				sub new_f {
957				my ($class, $str, $base) = @_;
958				my $r = Math::MPFR::Rmpfr_init2($PREC);
959				Math::MPFR::Rmpfr_set_str($r, $str, $base // 10, $ROUND);
960				bless \$r, $class;
961				}
962
963				sub new_c {
964				my ($class, $real, $imag, $base) = @_;
965
966				my $c = Math::MPC::Rmpc_init2($PREC);
967
968				if (defined($imag)) {
969				my $re = Math::MPFR::Rmpfr_init2($PREC);
970				my $im = Math::MPFR::Rmpfr_init2($PREC);
971
972				Math::MPFR::Rmpfr_set_str($re, $real, $base // 10, $ROUND);
973				Math::MPFR::Rmpfr_set_str($im, $imag, $base // 10, $ROUND);
974
975				Math::MPC::Rmpc_set_fr_fr($c, $re, $im, $ROUND);
976				}
977				else {
978				Math::MPC::Rmpc_set_str($c, $real, $base // 10, $ROUND);
979				}
980
981				bless \$c, $class;
982				}
983
984				sub _nan {
985				state $nan = do {
986				my $r = Math::MPFR::Rmpfr_init2($PREC);
987				Math::MPFR::Rmpfr_set_nan($r);
988				$r;
989				};
990				}
991
992				sub nan {
993				state $nan = do {
994				my $r = Math::MPFR::Rmpfr_init2($PREC);
995				Math::MPFR::Rmpfr_set_nan($r);
996				bless \$r;
997				};
998				}
999
1000				sub _inf {
1001				state $inf = do {
1002				my $r = Math::MPFR::Rmpfr_init2($PREC);
1003				Math::MPFR::Rmpfr_set_inf($r, 1);
1004				$r;
1005				};
1006				}
1007
1008				sub inf {
1009				state $inf = do {
1010				my $r = Math::MPFR::Rmpfr_init2($PREC);
1011				Math::MPFR::Rmpfr_set_inf($r, 1);
1012				bless \$r;
1013				};
1014				}
1015
1016				sub _ninf {
1017				state $ninf = do {
1018				my $r = Math::MPFR::Rmpfr_init2($PREC);
1019				Math::MPFR::Rmpfr_set_inf($r, -1);
1020				$r;
1021				};
1022				}
1023
1024				sub ninf {
1025				state $ninf = do {
1026				my $r = Math::MPFR::Rmpfr_init2($PREC);
1027				Math::MPFR::Rmpfr_set_inf($r, -1);
1028				bless \$r;
1029				};
1030				}
1031
1032				sub _zero {
1033				state $zero = Math::GMPz::Rmpz_init_set_ui(0);
1034				}
1035
1036				sub zero {
1037				state $zero = do {
1038				my $r = Math::GMPz::Rmpz_init_set_ui(0);
1039				bless \$r;
1040				};
1041				}
1042
1043				sub _one {
1044				state $one = Math::GMPz::Rmpz_init_set_ui(1);
1045				}
1046
1047				sub one {
1048				state $one = do {
1049				my $r = Math::GMPz::Rmpz_init_set_ui(1);
1050				bless \$r;
1051				};
1052				}
1053
1054				sub _mone {
1055				state $mone = Math::GMPz::Rmpz_init_set_si(-1);
1056				}
1057
1058				sub mone {
1059				state $mone = do {
1060				my $r = Math::GMPz::Rmpz_init_set_si(-1);
1061				bless \$r;
1062				};
1063				}
1064
1065				#
1066				## CONSTANTS
1067				#
1068
1069				sub pi {
1070				my $pi = Math::MPFR::Rmpfr_init2($PREC);
1071				Math::MPFR::Rmpfr_const_pi($pi, $ROUND);
1072				bless \$pi;
1073				}
1074
1075				sub tau {
1076				my $tau = Math::MPFR::Rmpfr_init2($PREC);
1077				Math::MPFR::Rmpfr_const_pi($tau, $ROUND);
1078				Math::MPFR::Rmpfr_mul_2ui($tau, $tau, 1, $ROUND);
1079				bless \$tau;
1080				}
1081
1082				sub ln2 {
1083				my $ln2 = Math::MPFR::Rmpfr_init2($PREC);
1084				Math::MPFR::Rmpfr_const_log2($ln2, $ROUND);
1085				bless \$ln2;
1086				}
1087
1088				sub euler {
1089				my $euler = Math::MPFR::Rmpfr_init2($PREC);
1090				Math::MPFR::Rmpfr_const_euler($euler, $ROUND);
1091				bless \$euler;
1092				}
1093
1094				sub catalan {
1095				my $catalan = Math::MPFR::Rmpfr_init2($PREC);
1096				Math::MPFR::Rmpfr_const_catalan($catalan, $ROUND);
1097				bless \$catalan;
1098				}
1099
1100				sub i {
1101				my $i = Math::MPC::Rmpc_init2($PREC);
1102				Math::MPC::Rmpc_set_ui_ui($i, 0, 1, $ROUND);
1103				bless \$i;
1104				}
1105
1106				sub e {
1107				state $one_f = (Math::MPFR::Rmpfr_init_set_ui_nobless(1, $ROUND))[0];
1108				my $e = Math::MPFR::Rmpfr_init2($PREC);
1109				Math::MPFR::Rmpfr_exp($e, $one_f, $ROUND);
1110				bless \$e;
1111				}
1112
1113				sub phi {
1114				state $five4_f = (Math::MPFR::Rmpfr_init_set_d_nobless(1.25, $ROUND))[0];
1115
1116				my $phi = Math::MPFR::Rmpfr_init2($PREC);
1117				Math::MPFR::Rmpfr_sqrt($phi, $five4_f, $ROUND);
1118				Math::MPFR::Rmpfr_add_d($phi, $phi, 0.5, $ROUND);
1119
1120				bless \$phi;
1121				}
1122
1123				#
1124				## OTHER
1125				#
1126
1127				sub stringify { # used in overloading
1128				require Math::AnyNum::stringify;
1129				(@_) = (${$_[0]});
1130				goto &__stringify__;
1131				}
1132
1133				sub numify { # used in overloading
1134				require Math::AnyNum::numify;
1135				(@_) = (${$_[0]});
1136				goto &__numify__;
1137				}
1138
1139				sub boolify { # used in overloading
1140				require Math::AnyNum::boolify;
1141				(@_) = (${$_[0]});
1142				goto &__boolify__;
1143				}
1144
1145				#
1146				## EQUALITY
1147				#
1148
1149				sub eq { # used in overloading
1150				require Math::AnyNum::eq;
1151				my ($x, $y) = @_;
1152
1153				if (ref($y) eq __PACKAGE__) {
1154				(@_) = ($$x, $$y);
1155				goto &__eq__;
1156				}
1157
1158				if (!ref($y)) {
1159				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1160				(@_) = ($$x, $y);
1161				}
1162				else {
1163				(@_) = ($$x, _str2obj($y));
1164				}
1165				goto &__eq__;
1166				}
1167
1168				(@_) = ($$x, _star2obj($y));
1169				goto &__eq__;
1170				}
1171
1172				#
1173				## INEQUALITY
1174				#
1175
1176				sub ne { # used in overloading
1177				require Math::AnyNum::ne;
1178				my ($x, $y) = @_;
1179
1180				if (ref($y) eq __PACKAGE__) {
1181				(@_) = ($$x, $$y);
1182				goto &__ne__;
1183				}
1184
1185				if (!ref($y)) {
1186				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1187				(@_) = ($$x, $y);
1188				}
1189				else {
1190				(@_) = ($$x, _str2obj($y));
1191				}
1192				goto &__ne__;
1193				}
1194
1195				(@_) = ($$x, _star2obj($y));
1196				goto &__ne__;
1197				}
1198
1199				#
1200				## COMPARISON
1201				#
1202
1203				sub cmp ($$) {
1204				require Math::AnyNum::cmp;
1205				my ($x, $y) = @_;
1206
1207				if (ref($y) eq __PACKAGE__) {
1208				(@_) = ($$x, $$y);
1209				goto &__cmp__;
1210				}
1211
1212				if (!ref($y)) {
1213				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1214				(@_) = ($$x, $y);
1215				}
1216				else {
1217				(@_) = ($$x, _str2obj($y));
1218				}
1219				goto &__cmp__;
1220				}
1221
1222				(@_) = ($$x, _star2obj($y));
1223				goto &__cmp__;
1224				}
1225
1226				sub acmp ($$) {
1227				require Math::AnyNum::abs;
1228				require Math::AnyNum::cmp;
1229				my ($x, $y) = @_;
1230
1231				if (!ref($y) and CORE::int($y) eq $y and $y >= 0 and $y < ULONG_MAX) {
1232				## `y` is a native unsigned integer
1233				}
1234				else {
1235				$y = __abs__(ref($y) eq __PACKAGE__ ? $$y : _star2obj($y));
1236				}
1237
1238				__cmp__(__abs__(ref($x) eq __PACKAGE__ ? $$x : _star2obj($x)), $y);
1239				}
1240
1241				#
1242				## GREATER THAN
1243				#
1244
1245				sub gt { # used in overloading
1246				require Math::AnyNum::cmp;
1247				my ($x, $y) = @_;
1248
1249				if (ref($y) eq __PACKAGE__) {
1250				return ((__cmp__($$x, $$y) // return undef) > 0);
1251				}
1252
1253				if (!ref($y)) {
1254				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1255				return ((__cmp__($$x, $y) // return undef) > 0);
1256				}
1257				return ((__cmp__($$x, _str2obj($y)) // return undef) > 0);
1258				}
1259
1260				(__cmp__($$x, _star2obj($y)) // return undef) > 0;
1261				}
1262
1263				#
1264				## EQUAL OR GREATER THAN
1265				#
1266
1267				sub ge { # used in overloading
1268				require Math::AnyNum::cmp;
1269				my ($x, $y) = @_;
1270
1271				if (ref($y) eq __PACKAGE__) {
1272				return ((__cmp__($$x, $$y) // return undef) >= 0);
1273				}
1274
1275				if (!ref($y)) {
1276				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1277				return ((__cmp__($$x, $y) // return undef) >= 0);
1278				}
1279				return ((__cmp__($$x, _str2obj($y)) // return undef) >= 0);
1280				}
1281
1282				(__cmp__($$x, _star2obj($y)) // return undef) >= 0;
1283				}
1284
1285				#
1286				## LESS THAN
1287				#
1288
1289				sub lt { # used in overloading
1290				require Math::AnyNum::cmp;
1291				my ($x, $y) = @_;
1292
1293				if (ref($y) eq __PACKAGE__) {
1294				return ((__cmp__($$x, $$y) // return undef) < 0);
1295				}
1296
1297				if (!ref($y)) {
1298				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1299				return ((__cmp__($$x, $y) // return undef) < 0);
1300				}
1301				return ((__cmp__($$x, _str2obj($y)) // return undef) < 0);
1302				}
1303
1304				(__cmp__($$x, _star2obj($y)) // return undef) < 0;
1305				}
1306
1307				#
1308				## EQUAL OR LESS THAN
1309				#
1310
1311				sub le { # used in overloading
1312				require Math::AnyNum::cmp;
1313				my ($x, $y) = @_;
1314
1315				if (ref($y) eq __PACKAGE__) {
1316				return ((__cmp__($$x, $$y) // return undef) <= 0);
1317				}
1318
1319				if (!ref($y)) {
1320				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1321				return ((__cmp__($$x, $y) // return undef) <= 0);
1322				}
1323				return ((__cmp__($$x, _str2obj($y)) // return undef) <= 0);
1324				}
1325
1326				(__cmp__($$x, _star2obj($y)) // return undef) <= 0;
1327				}
1328
1329				#
1330				## COPY
1331				#
1332
1333				sub _copy {
1334				my ($x) = @_;
1335				my $ref = ref($x);
1336
1337				if ($ref eq 'Math::GMPz') {
1338				Math::GMPz::Rmpz_init_set($x);
1339				}
1340				elsif ($ref eq 'Math::MPFR') {
1341				my $r = Math::MPFR::Rmpfr_init2($PREC);
1342				Math::MPFR::Rmpfr_set($r, $x, $ROUND);
1343				$r;
1344				}
1345				elsif ($ref eq 'Math::GMPq') {
1346				my $r = Math::GMPq::Rmpq_init();
1347				Math::GMPq::Rmpq_set($r, $x);
1348				$r;
1349				}
1350				elsif ($ref eq 'Math::MPC') {
1351				my $r = Math::MPC::Rmpc_init2($PREC);
1352				Math::MPC::Rmpc_set($r, $x, $ROUND);
1353				$r;
1354				}
1355				else {
1356				_str2obj("$x"); # this should not happen
1357				}
1358				}
1359
1360				sub copy ($) {
1361				my ($x) = @_;
1362				bless \_copy($$x);
1363				}
1364
1365				#
1366				## CONVERSION TO INTEGER
1367				#
1368
1369				sub int { # used in overloading
1370				my ($x) = @_;
1371
1372				bless \(
1373				(
1374				ref($x) eq __PACKAGE__
1375				? ref($$x) eq 'Math::GMPz'
1376				? (return $x)
1377				: _any2mpz($$x)
1378				: _star2mpz($x)
1379				) // goto &nan
1380				);
1381				}
1382
1383				#
1384				## CONVERSION TO RATIONAL
1385				#
1386
1387				sub rat ($) {
1388				my ($x) = @_;
1389				if (ref($x) eq __PACKAGE__) {
1390				ref($$x) eq 'Math::GMPq' && return $x;
1391				bless \(_any2mpq($$x) // (goto &nan));
1392				}
1393				else {
1394
1395				# Parse a decimal number as an exact fraction
1396				if ("$x" =~ /^([+-]?+(?=\.?[0-9])[0-9_]*+(?:\.[0-9_]++)?(?:[Ee](?:[+-]?+[0-9_]+))?)\z/) {
1397				my $frac = _str2frac(lc($1));
1398				my $q = Math::GMPq::Rmpq_init();
1399				Math::GMPq::Rmpq_set_str($q, $frac, 10);
1400				Math::GMPq::Rmpq_canonicalize($q) if (index($frac, '/') != -1);
1401				return bless \$q;
1402				}
1403
1404				my $r = _star2obj($x);
1405				ref($r) eq 'Math::GMPq' && return bless \$r;
1406				bless(\_any2mpq($r) // goto &nan);
1407				}
1408				}
1409
1410				#
1411				## CONVERSION TO FLOATING-POINT
1412				#
1413
1414				sub float ($) {
1415				my ($x) = @_;
1416
1417				bless \(
1418				ref($x) eq __PACKAGE__
1419				? ref($$x) eq 'Math::MPFR'
1420				? (return $x)
1421				: _any2mpfr($$x)
1422				: _star2mpfr($x)
1423				);
1424				}
1425
1426				#
1427				## CONVERSION TO COMPLEX
1428				#
1429
1430				sub complex ($) {
1431				my ($x) = @_;
1432				bless \(
1433				ref($x) eq __PACKAGE__
1434				? ref($$x) eq 'Math::MPC'
1435				? (return $x)
1436				: _any2mpc($$x)
1437				: _any2mpc(_star2obj($x))
1438				);
1439				}
1440
1441				#
1442				## NEGATION
1443				#
1444
1445				sub neg { # used in overloading
1446				require Math::AnyNum::neg;
1447				my ($x) = @_;
1448				bless \__neg__(ref($x) eq __PACKAGE__ ? $$x : _star2obj($x));
1449				}
1450
1451				#
1452				## ABSOLUTE VALUE
1453				#
1454
1455				sub abs { # used in overloading
1456				require Math::AnyNum::abs;
1457				my ($x) = @_;
1458				bless \__abs__(ref($x) eq __PACKAGE__ ? $$x : _star2obj($x));
1459				}
1460
1461				#
1462				## MULTIPLICATIVE INVERSE
1463				#
1464
1465				sub inv ($) {
1466				require Math::AnyNum::inv;
1467				my ($x) = @_;
1468				bless \__inv__(ref($x) eq __PACKAGE__ ? $$x : _star2obj($x));
1469				}
1470
1471				#
1472				## INCREMENTATION BY ONE
1473				#
1474
1475				sub inc ($) {
1476				require Math::AnyNum::inc;
1477				my ($x) = @_;
1478				bless \__inc__($$x);
1479				}
1480
1481				#
1482				## DECREMENTATION BY ONE
1483				#
1484
1485				sub dec ($) {
1486				require Math::AnyNum::dec;
1487				my ($x) = @_;
1488				bless \__dec__($$x);
1489				}
1490
1491				sub conj ($) {
1492				my ($x) = @_;
1493
1494				if (ref($x) ne __PACKAGE__) {
1495				$x = __PACKAGE__->new($x);
1496				}
1497
1498				if (ref($$x) eq 'Math::MPC') {
1499				my $r = Math::MPC::Rmpc_init2($PREC);
1500				Math::MPC::Rmpc_conj($r, $$x, $ROUND);
1501				bless \$r;
1502				}
1503				else {
1504				$x;
1505				}
1506				}
1507
1508				sub real ($) {
1509				my ($x) = @_;
1510
1511				if (ref($x) ne __PACKAGE__) {
1512				$x = __PACKAGE__->new($x);
1513				}
1514
1515				if (ref($$x) eq 'Math::MPC') {
1516				my $r = Math::MPFR::Rmpfr_init2($PREC);
1517				Math::MPC::RMPC_RE($r, $$x);
1518				bless \$r;
1519				}
1520				else {
1521				$x;
1522				}
1523				}
1524
1525				sub imag ($) {
1526				my ($x) = @_;
1527
1528				if (ref($x) ne __PACKAGE__) {
1529				$x = __PACKAGE__->new($x);
1530				}
1531
1532				if (ref($$x) eq 'Math::MPC') {
1533				my $r = Math::MPFR::Rmpfr_init2($PREC);
1534				Math::MPC::RMPC_IM($r, $$x);
1535				bless \$r;
1536				}
1537				else {
1538				goto &zero;
1539				}
1540				}
1541
1542				sub reals ($) {
1543				my ($x) = @_;
1544
1545				if (ref($x) ne __PACKAGE__) {
1546				$x = __PACKAGE__->new($x);
1547				}
1548
1549				($x->real, $x->imag);
1550				}
1551
1552				#
1553				## ADDITION
1554				#
1555
1556				sub add { # used in overloading
1557				require Math::AnyNum::add;
1558				my ($x, $y) = @_;
1559
1560				if (ref($y) eq __PACKAGE__) {
1561				return bless \__add__($$x, $$y);
1562				}
1563
1564				$x = $$x;
1565
1566				if (!ref($y)) {
1567				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1568				if (ref($x) eq 'Math::GMPq') {
1569				my $r = Math::GMPq::Rmpq_init();
1570				$y < 0
1571				? Math::GMPq::Rmpq_set_si($r, $y, 1)
1572				: Math::GMPq::Rmpq_set_ui($r, $y, 1);
1573				Math::GMPq::Rmpq_add($r, $r, $x);
1574				return bless \$r;
1575				}
1576
1577				return bless \__add__($x, $y);
1578				}
1579
1580				return bless \__add__($x, _str2obj($y));
1581				}
1582
1583				bless \__add__($x, _star2obj($y));
1584				}
1585
1586				#
1587				## SUBTRACTION
1588				#
1589
1590				sub sub { # used in overloading
1591				require Math::AnyNum::sub;
1592				my ($x, $y) = @_;
1593
1594				$x =
1595				ref($x) eq __PACKAGE__ ? $$x
1596				: ref($x) ? _star2obj($x)
1597				: _str2obj($x);
1598
1599				if (ref($y) eq __PACKAGE__) {
1600				return bless \__sub__($x, $$y);
1601				}
1602
1603				if (!ref($y)) {
1604				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1605				if (ref($x) eq 'Math::GMPq') {
1606				my $r = Math::GMPq::Rmpq_init();
1607				$y < 0
1608				? Math::GMPq::Rmpq_set_si($r, $y, 1)
1609				: Math::GMPq::Rmpq_set_ui($r, $y, 1);
1610				Math::GMPq::Rmpq_sub($r, $x, $r);
1611				return bless \$r;
1612				}
1613
1614				return bless \__sub__($x, $y);
1615				}
1616
1617				return bless \__sub__($x, _str2obj($y));
1618				}
1619
1620				bless \__sub__($x, _star2obj($y));
1621				}
1622
1623				#
1624				## MULTIPLICATION
1625				#
1626
1627				sub mul { # used in overloading
1628				require Math::AnyNum::mul;
1629				my ($x, $y) = @_;
1630
1631				if (ref($y) eq __PACKAGE__) {
1632				return bless \__mul__($$x, $$y);
1633				}
1634
1635				$x = $$x;
1636
1637				if (!ref($y)) {
1638				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1639				if (ref($x) eq 'Math::GMPq') {
1640				my $r = Math::GMPq::Rmpq_init();
1641				$y < 0
1642				? Math::GMPq::Rmpq_set_si($r, $y, 1)
1643				: Math::GMPq::Rmpq_set_ui($r, $y, 1);
1644				Math::GMPq::Rmpq_mul($r, $r, $x);
1645				return bless \$r;
1646				}
1647
1648				return bless \__mul__($x, $y);
1649				}
1650
1651				return bless \__mul__($x, _str2obj($y));
1652				}
1653
1654				bless \__mul__($x, _star2obj($y));
1655				}
1656
1657				#
1658				## DIVISION
1659				#
1660
1661				sub div { # used in overloading
1662				require Math::AnyNum::div;
1663				my ($x, $y) = @_;
1664
1665				$x =
1666				ref($x) eq __PACKAGE__ ? $$x
1667				: ref($x) ? _star2obj($x)
1668				: _str2obj($x);
1669
1670				if (ref($y) eq __PACKAGE__) {
1671				return bless \__div__($x, $$y);
1672				}
1673
1674				if (!ref($y)) {
1675				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN and CORE::int($y)) {
1676				if (ref($x) eq 'Math::GMPq') {
1677				my $r = Math::GMPq::Rmpq_init();
1678				$y < 0
1679				? Math::GMPq::Rmpq_set_si($r, -1, -$y)
1680				: Math::GMPq::Rmpq_set_ui($r, 1, $y);
1681				Math::GMPq::Rmpq_mul($r, $r, $x);
1682				return bless \$r;
1683				}
1684
1685				return bless \__div__($x, $y);
1686				}
1687
1688				return bless \__div__($x, _str2obj($y));
1689				}
1690
1691				bless \__div__($x, _star2obj($y));
1692				}
1693
1694				#
1695				## INTEGER ADDITION
1696				#
1697
1698				sub iadd ($$) {
1699				my ($x, $y) = @_;
1700
1701				if (!ref($x) and ref($y)) {
1702				($x, $y) = ($y, $x);
1703				}
1704
1705				$x = _star2mpz($x) // goto &nan;
1706
1707				if (!ref($y) and CORE::int($y) eq $y and CORE::abs($y) < ULONG_MAX) {
1708				my $r = Math::GMPz::Rmpz_init();
1709				$y < 0
1710				? Math::GMPz::Rmpz_sub_ui($r, $x, -$y)
1711				: Math::GMPz::Rmpz_add_ui($r, $x, $y);
1712				return bless \$r;
1713				}
1714
1715				$y = _star2mpz($y) // goto &nan;
1716
1717				my $r = Math::GMPz::Rmpz_init();
1718				Math::GMPz::Rmpz_add($r, $x, $y);
1719				bless \$r;
1720				}
1721
1722				#
1723				## INTEGER SUBTRACTION
1724				#
1725
1726				sub isub ($$) {
1727				my ($x, $y) = @_;
1728
1729				$x = _star2mpz($x) // goto &nan;
1730
1731				if (!ref($y) and CORE::int($y) eq $y and CORE::abs($y) < ULONG_MAX) {
1732				my $r = Math::GMPz::Rmpz_init();
1733				$y < 0
1734				? Math::GMPz::Rmpz_add_ui($r, $x, -$y)
1735				: Math::GMPz::Rmpz_sub_ui($r, $x, $y);
1736				return bless \$r;
1737				}
1738
1739				$y = _star2mpz($y) // goto &nan;
1740
1741				my $r = Math::GMPz::Rmpz_init();
1742				Math::GMPz::Rmpz_sub($r, $x, $y);
1743				bless \$r;
1744				}
1745
1746				#
1747				## INTEGER MULTIPLICATION
1748				#
1749
1750				sub imul ($$) {
1751				my ($x, $y) = @_;
1752
1753				if (!ref($x) and ref($y)) {
1754				($x, $y) = ($y, $x);
1755				}
1756
1757				$x = _star2mpz($x) // goto &nan;
1758
1759				if (!ref($y) and CORE::int($y) eq $y and CORE::abs($y) < ULONG_MAX) {
1760				my $r = Math::GMPz::Rmpz_init();
1761				Math::GMPz::Rmpz_mul_ui($r, $x, CORE::abs($y));
1762				Math::GMPz::Rmpz_neg($r, $r) if $y < 0;
1763				return bless \$r;
1764				}
1765
1766				$y = _star2mpz($y) // goto &nan;
1767
1768				my $r = Math::GMPz::Rmpz_init();
1769				Math::GMPz::Rmpz_mul($r, $x, $y);
1770				bless \$r;
1771				}
1772
1773				#
1774				## INTEGER DIVISION
1775				#
1776
1777				sub idiv ($$) {
1778				my ($x, $y) = @_;
1779
1780				$x = _star2mpz($x) // goto &nan;
1781
1782				if (!ref($y) and CORE::int($y) eq $y and CORE::int($y) and CORE::abs($y) < ULONG_MAX) {
1783				my $r = Math::GMPz::Rmpz_init();
1784				Math::GMPz::Rmpz_tdiv_q_ui($r, $x, CORE::abs($y));
1785				Math::GMPz::Rmpz_neg($r, $r) if $y < 0;
1786				return bless \$r;
1787				}
1788
1789				$y = _star2mpz($y) // goto &nan;
1790
1791				# Detect division by zero
1792				Math::GMPz::Rmpz_sgn($y) \|\| do {
1793				my $sign = Math::GMPz::Rmpz_sgn($x);
1794
1795				if ($sign == 0) { # 0/0
1796				goto &nan;
1797				}
1798				elsif ($sign > 0) { # x/0 where: x > 0
1799				goto &inf;
1800				}
1801				else { # x/0 where: x < 0
1802				goto &ninf;
1803				}
1804				};
1805
1806				my $r = Math::GMPz::Rmpz_init();
1807				Math::GMPz::Rmpz_tdiv_q($r, $x, $y);
1808				bless \$r;
1809				}
1810
1811				#
1812				## POWER
1813				#
1814
1815				sub pow ($$) {
1816				require Math::AnyNum::pow;
1817				my ($x, $y) = @_;
1818
1819				$x =
1820				ref($x) eq __PACKAGE__ ? $$x
1821				: ref($x) ? _star2obj($x)
1822				: _str2obj($x);
1823
1824				if (ref($y) eq __PACKAGE__) {
1825				return bless \__pow__($x, $$y);
1826				}
1827
1828				if (!ref($y)) {
1829				if (CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
1830				return bless \__pow__($x, $y);
1831				}
1832
1833				return bless \__pow__($x, _str2obj($y));
1834				}
1835
1836				bless \__pow__($x, _star2obj($y));
1837				}
1838
1839				#
1840				## INTEGER POWER
1841				#
1842
1843				sub ipow ($$) {
1844				my ($x, $y) = @_;
1845
1846				# Both `x` and `y` are unsigned native integers
1847				if ( !ref($x)
1848				and !ref($y)
1849				and CORE::int($x) eq $x
1850				and $x >= 0
1851				and $x < ULONG_MAX
1852				and CORE::int($y) eq $y
1853				and $y >= 0
1854				and $y < ULONG_MAX) {
1855
1856				my $r = Math::GMPz::Rmpz_init();
1857				Math::GMPz::Rmpz_ui_pow_ui($r, $x, $y);
1858				return bless \$r;
1859				}
1860
1861				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // (goto &nan);
1862
1863				if (!ref($y) and CORE::int($y) eq $y and CORE::abs($y) < ULONG_MAX) {
1864				## `y` is already a native integer
1865				}
1866				else {
1867				$y = _any2si(ref($y) eq __PACKAGE__ ? $$y : _star2obj($y)) // (goto &nan);
1868				}
1869
1870				my $r = Math::GMPz::Rmpz_init();
1871				Math::GMPz::Rmpz_pow_ui($r, $x, CORE::abs($y));
1872
1873				if ($y < 0) {
1874				Math::GMPz::Rmpz_sgn($r) \|\| goto &inf; # 0^(-y) = Inf
1875				state $ONE_Z = Math::GMPz::Rmpz_init_set_ui_nobless(1);
1876				Math::GMPz::Rmpz_tdiv_q($r, $ONE_Z, $r);
1877				}
1878
1879				bless \$r;
1880				}
1881
1882				#
1883				## IPOW2
1884				#
1885
1886				sub ipow2 ($) {
1887				my ($n) = @_;
1888
1889				if (ref($n) eq __PACKAGE__) {
1890				$n = _any2si($$n) // goto &nan;
1891				}
1892				elsif ( !ref($n)
1893				and CORE::int($n) eq $n
1894				and $n > LONG_MIN
1895				and $n < ULONG_MAX) {
1896				## `n` is already a native integer
1897				}
1898				else {
1899				$n = _any2si(_star2obj($n)) // goto &nan;
1900				}
1901
1902				goto &zero if $n < 0;
1903				state $one = Math::GMPz::Rmpz_init_set_ui_nobless(1);
1904
1905				my $r = Math::GMPz::Rmpz_init();
1906				Math::GMPz::Rmpz_mul_2exp($r, $one, $n);
1907				bless \$r;
1908				}
1909
1910				#
1911				## IPOW10
1912				#
1913
1914				sub ipow10 ($) {
1915				my ($n) = @_;
1916
1917				if (ref($n) eq __PACKAGE__) {
1918				$n = _any2si($$n) // goto &nan;
1919				}
1920				elsif ( !ref($n)
1921				and CORE::int($n) eq $n
1922				and $n > LONG_MIN
1923				and $n < ULONG_MAX) {
1924				## $n is a native integer
1925				}
1926				else {
1927				$n = _any2si(_star2obj($n)) // goto &nan;
1928				}
1929
1930				goto &zero if $n < 0;
1931
1932				my $r = Math::GMPz::Rmpz_init();
1933				Math::GMPz::Rmpz_ui_pow_ui($r, 10, $n);
1934				bless \$r;
1935				}
1936
1937				#
1938				## ROOT
1939				#
1940
1941				sub root ($$) {
1942				require Math::AnyNum::pow;
1943				require Math::AnyNum::inv;
1944				my ($x, $y) = @_;
1945
1946				$x =
1947				ref($x) eq __PACKAGE__ ? $$x
1948				: ref($x) ? _star2obj($x)
1949				: _str2obj($x);
1950
1951				$y =
1952				ref($y) eq __PACKAGE__ ? $$y
1953				: ref($y) ? _star2obj($y)
1954				: _str2obj($y);
1955
1956				bless \__pow__($x, __inv__($y));
1957				}
1958
1959				#
1960				## Polygonal root
1961				#
1962
1963				sub polygonal_root ($$) {
1964				require Math::AnyNum::polygonal_root;
1965				bless \__polygonal_root__(_star2mpfr_mpc($_[0]), _star2mpfr_mpc($_[1]));
1966				}
1967
1968				#
1969				## Second polygonal root
1970				#
1971
1972				sub polygonal_root2 ($$) {
1973				require Math::AnyNum::polygonal_root;
1974				bless \__polygonal_root__(_star2mpfr_mpc($_[0]), _star2mpfr_mpc($_[1]), 1);
1975				}
1976
1977				#
1978				## isqrt
1979				#
1980
1981				sub isqrt ($) {
1982				my ($x) = @_;
1983
1984				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
1985
1986				Math::GMPz::Rmpz_sgn($x) < 0 and goto &nan;
1987				my $r = Math::GMPz::Rmpz_init();
1988				Math::GMPz::Rmpz_sqrt($r, $x);
1989				bless \$r;
1990				}
1991
1992				#
1993				## icbrt
1994				#
1995
1996				sub icbrt ($) {
1997				my ($x) = @_;
1998				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
1999				my $r = Math::GMPz::Rmpz_init();
2000				Math::GMPz::Rmpz_root($r, $x, 3);
2001				bless \$r;
2002				}
2003
2004				#
2005				## IROOT
2006				#
2007
2008				sub iroot ($$) {
2009				my ($x, $y) = @_;
2010
2011				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
2012
2013				if (!ref($y) and CORE::int($y) eq $y and CORE::abs($y) < ULONG_MAX) {
2014				## `y`is native integer
2015				}
2016				elsif (ref($y) eq __PACKAGE__) {
2017				$y = _any2si($$y) // goto &nan;
2018				}
2019				else {
2020				$y = _any2si(_star2obj($y)) // goto &nan;
2021				}
2022
2023				if ($y == 0) {
2024				Math::GMPz::Rmpz_sgn($x) \|\| goto &zero; # 0^Inf = 0
2025
2026				# 1^Inf = 1 ; (-1)^Inf = 1
2027				if (Math::GMPz::Rmpz_cmpabs_ui($x, 1) == 0) {
2028				goto &one;
2029				}
2030
2031				goto &inf;
2032				}
2033
2034				if ($y < 0) {
2035				my $sign = Math::GMPz::Rmpz_sgn($x)
2036				\|\| goto &inf; # 1 / 0^k = Inf
2037
2038				if ($sign < 0) {
2039				goto &nan;
2040				}
2041
2042				if (Math::GMPz::Rmpz_cmp_ui($x, 1) == 0) { # 1 / 1^k = 1
2043				goto &one;
2044				}
2045
2046				goto &zero;
2047				}
2048
2049				if ($y % 2 == 0 and Math::GMPz::Rmpz_sgn($x) < 0) {
2050				goto &nan;
2051				}
2052
2053				my $r = Math::GMPz::Rmpz_init();
2054				$y == 2
2055				? Math::GMPz::Rmpz_sqrt($r, $x)
2056				: Math::GMPz::Rmpz_root($r, $x, $y);
2057				bless \$r;
2058				}
2059
2060				#
2061				## ISQRTREM
2062				#
2063
2064				sub isqrtrem ($) {
2065				my ($x) = @_;
2066
2067				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // return (nan(), nan());
2068
2069				Math::GMPz::Rmpz_sgn($x) < 0
2070				and return (nan(), nan());
2071
2072				my $r = Math::GMPz::Rmpz_init();
2073				my $s = Math::GMPz::Rmpz_init();
2074
2075				Math::GMPz::Rmpz_sqrtrem($r, $s, $x);
2076
2077				((bless \$r), (bless \$s));
2078				}
2079
2080				#
2081				## IROOTREM
2082				#
2083
2084				sub irootrem ($$) {
2085				my ($x, $y) = @_;
2086
2087				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // return (nan(), nan());
2088
2089				if (!ref($y) and CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
2090				## `y` is a native integer
2091				}
2092				else {
2093				$y = _any2si(ref($y) eq __PACKAGE__ ? $$y : _star2obj($y)) // (return (nan(), nan()));
2094				}
2095
2096				if ($y == 0) {
2097
2098				# 0^Inf = 0
2099				if (Math::GMPz::Rmpz_sgn($x) == 0) {
2100				return (zero(), mone());
2101				}
2102
2103				my $r = Math::GMPz::Rmpz_init();
2104				Math::GMPz::Rmpz_sub_ui($r, $x, 1);
2105
2106				# 1^Inf = 1 ; (-1)^Inf = 1
2107				if (Math::GMPz::Rmpz_cmpabs_ui($x, 1) == 0) {
2108				return (one(), (bless \$r));
2109				}
2110
2111				return (inf(), (bless \$r));
2112				}
2113
2114				if ($y < 0) {
2115				my $sgn = Math::GMPz::Rmpz_sgn($x);
2116
2117				# 1 / 0^k = Inf
2118				if ($sgn == 0) {
2119				return (inf(), zero());
2120				}
2121
2122				# 1 / 1^k = 1
2123				if (Math::GMPz::Rmpz_cmp_ui($x, 1) == 0) {
2124				return (one(), zero());
2125				}
2126
2127				# x is negative
2128				if ($sgn < 0) {
2129				return (nan(), nan());
2130				}
2131
2132				return (zero(), ninf());
2133				}
2134
2135				if ($y % 2 == 0 and Math::GMPz::Rmpz_sgn($x) < 0) {
2136				return (nan(), nan());
2137				}
2138
2139				my $r = Math::GMPz::Rmpz_init();
2140				my $s = Math::GMPz::Rmpz_init();
2141
2142				$y == 2
2143				? Math::GMPz::Rmpz_sqrtrem($r, $s, $x)
2144				: Math::GMPz::Rmpz_rootrem($r, $s, $x, $y);
2145
2146				((bless \$r), (bless \$s));
2147				}
2148
2149				#
2150				## MOD
2151				#
2152
2153				sub mod ($$) {
2154				require Math::AnyNum::mod;
2155				my ($x, $y) = @_;
2156
2157				$x =
2158				ref($x) eq __PACKAGE__ ? $$x
2159				: ref($x) ? _star2obj($x)
2160				: _str2obj($x);
2161
2162				if (ref($y) eq __PACKAGE__) {
2163				return bless \__mod__($x, $$y);
2164				}
2165
2166				if (!ref($y)) {
2167
2168				if ( ref($x) ne 'Math::GMPq'
2169				and CORE::int($y) eq $y
2170				and $y > 0
2171				and $y < ULONG_MAX) {
2172				return bless \__mod__($x, $y);
2173				}
2174
2175				return bless \__mod__($x, _str2obj($y));
2176				}
2177
2178				bless \__mod__($x, _star2obj($y));
2179				}
2180
2181				#
2182				## IMOD
2183				#
2184
2185				sub imod ($$) {
2186				my ($x, $y) = @_;
2187
2188				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // (goto &nan);
2189
2190				if (!ref($y) and CORE::int($y) eq $y and CORE::abs($y) < ULONG_MAX) {
2191
2192				CORE::int($y) \|\| goto &nan;
2193
2194				my $neg_y = $y < 0;
2195				$y = -$y if $neg_y;
2196
2197				my $r = Math::GMPz::Rmpz_init();
2198				Math::GMPz::Rmpz_mod_ui($r, $x, $y);
2199
2200				if (!Math::GMPz::Rmpz_sgn($r)) {
2201				## OK
2202				}
2203				elsif ($neg_y) {
2204				Math::GMPz::Rmpz_sub_ui($r, $r, $y);
2205				}
2206
2207				return bless \$r;
2208				}
2209
2210				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // goto &nan;
2211
2212				my $sign_y = Math::GMPz::Rmpz_sgn($y) \|\| goto &nan;
2213
2214				my $r = Math::GMPz::Rmpz_init();
2215				Math::GMPz::Rmpz_mod($r, $x, $y);
2216
2217				if (!Math::GMPz::Rmpz_sgn($r)) {
2218				## OK
2219				}
2220				elsif ($sign_y < 0) {
2221				Math::GMPz::Rmpz_add($r, $r, $y);
2222				}
2223
2224				bless \$r;
2225				}
2226
2227				#
2228				## DIVMOD
2229				#
2230
2231				sub divmod ($$) {
2232				my ($x, $y) = @_;
2233
2234				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // return (nan(), nan());
2235				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // return (nan(), nan());
2236
2237				Math::GMPz::Rmpz_sgn($y)
2238				\|\| return (nan(), nan());
2239
2240				my $r = Math::GMPz::Rmpz_init();
2241				my $s = Math::GMPz::Rmpz_init();
2242
2243				Math::GMPz::Rmpz_divmod($r, $s, $x, $y);
2244
2245				((bless \$r), (bless \$s));
2246				}
2247
2248				#
2249				## is_div
2250				#
2251
2252				sub is_div ($$) {
2253				require Math::AnyNum::eq;
2254				my ($x, $y) = @_;
2255
2256				if (ref($x) eq __PACKAGE__ and ref($$x) eq 'Math::GMPz') {
2257				if (ref($y)) {
2258				if (ref($y) eq __PACKAGE__ and ref($$y) eq 'Math::GMPz') {
2259				return (Math::GMPz::Rmpz_divisible_p($$x, $$y) && Math::GMPz::Rmpz_sgn($$y));
2260				}
2261				}
2262				elsif (CORE::int($y) eq $y and $y and CORE::abs($y) < ULONG_MAX) {
2263				return Math::GMPz::Rmpz_divisible_ui_p($$x, CORE::abs($y));
2264				}
2265				}
2266
2267				(@_) = (${mod($x, $y)}, 0);
2268				goto &__eq__;
2269				}
2270
2271				#
2272				## SPECIAL
2273				#
2274
2275				sub ln { # used in overloading
2276				require Math::AnyNum::log;
2277				bless \__log__(_star2mpfr_mpc($_[0]));
2278				}
2279
2280				sub log2 ($) {
2281				require Math::AnyNum::log;
2282				bless \__log2__(_star2mpfr_mpc($_[0]));
2283				}
2284
2285				sub log10 ($) {
2286				require Math::AnyNum::log;
2287				bless \__log10__(_star2mpfr_mpc($_[0]));
2288				}
2289
2290				sub length ($) {
2291				my ($z) = _star2mpz($_[0]) // return -1;
2292				CORE::length(Math::GMPz::Rmpz_get_str($z, 10)) - (Math::GMPz::Rmpz_sgn($z) < 0 ? 1 : 0);
2293				}
2294
2295				sub log (_;$) {
2296				require Math::AnyNum::log;
2297				my ($x, $y) = @_;
2298
2299				if (!defined($y)) {
2300				return bless \__log__(_star2mpfr_mpc($x));
2301				}
2302
2303				require Math::AnyNum::div;
2304				bless \__div__(__log__(_star2mpfr_mpc($x)), __log__(_star2mpfr_mpc($y)));
2305				}
2306
2307				#
2308				## ILOG
2309				#
2310
2311				sub ilog2 ($) {
2312				require Math::AnyNum::ilog;
2313				state $two = Math::GMPz::Rmpz_init_set_ui(2);
2314				bless \__ilog__((_star2mpz($_[0]) // goto &nan), $two);
2315				}
2316
2317				sub ilog10 ($) {
2318				require Math::AnyNum::ilog;
2319				state $ten = Math::GMPz::Rmpz_init_set_ui(10);
2320				bless \__ilog__((_star2mpz($_[0]) // goto &nan), $ten);
2321				}
2322
2323				sub ilog ($;$) {
2324				my ($x, $y) = @_;
2325
2326				if (!defined($y)) {
2327				require Math::AnyNum::log;
2328				return bless \(_any2mpz(__log__(_star2mpfr_mpc($x))) // goto &nan);
2329				}
2330
2331				require Math::AnyNum::ilog;
2332				bless \__ilog__((_star2mpz($x) // goto &nan), (_star2mpz($y) // goto &nan));
2333				}
2334
2335				#
2336				## SQRT
2337				#
2338
2339				sub sqrt { # used in overloading
2340				require Math::AnyNum::sqrt;
2341				bless \__sqrt__(_star2mpfr_mpc($_[0]));
2342				}
2343
2344				sub cbrt ($) {
2345				require Math::AnyNum::cbrt;
2346				bless \__cbrt__(_star2mpfr_mpc($_[0]));
2347				}
2348
2349				sub sqr ($) {
2350				require Math::AnyNum::mul;
2351				my ($x) = @_;
2352
2353				$x =
2354				ref($x) eq __PACKAGE__
2355				? $$x
2356				: _star2obj($x);
2357
2358				bless \__mul__($x, $x);
2359				}
2360
2361				sub norm ($) {
2362				require Math::AnyNum::norm;
2363				my ($x) = @_;
2364
2365				$x =
2366				ref($x) eq __PACKAGE__
2367				? $$x
2368				: _star2obj($x);
2369
2370				bless \__norm__($x);
2371				}
2372
2373				sub exp { # used in overloading
2374				require Math::AnyNum::exp;
2375				bless \__exp__(_star2mpfr_mpc($_[0]));
2376				}
2377
2378				sub exp2 ($) {
2379				require Math::AnyNum::pow;
2380				my ($x) = @_;
2381
2382				state $base = Math::GMPz::Rmpz_init_set_ui(2);
2383
2384				if (ref($x) eq __PACKAGE__) {
2385				bless \__pow__($base, $$x);
2386				}
2387				elsif (!ref($x) and CORE::int($x) eq $x and $x > LONG_MIN and $x < ULONG_MAX) {
2388				bless \__pow__($base, $x);
2389				}
2390				else {
2391				bless \__pow__($base, _star2obj($x));
2392				}
2393				}
2394
2395				sub exp10 ($) {
2396				require Math::AnyNum::pow;
2397				my ($x) = @_;
2398
2399				state $base = Math::GMPz::Rmpz_init_set_ui(10);
2400
2401				if (ref($x) eq __PACKAGE__) {
2402				bless \__pow__($base, $$x);
2403				}
2404				elsif (!ref($x) and CORE::int($x) eq $x and $x > LONG_MIN and $x < ULONG_MAX) {
2405				bless \__pow__($base, $x);
2406				}
2407				else {
2408				bless \__pow__($base, _star2obj($x));
2409				}
2410				}
2411
2412				sub floor ($) {
2413				require Math::AnyNum::floor;
2414				my ($x) = @_;
2415
2416				if (ref($x) ne __PACKAGE__) {
2417				$x = __PACKAGE__->new($x);
2418				}
2419
2420				ref($$x) eq 'Math::GMPz' and return $x; # already an integer
2421				bless \__floor__($$x);
2422				}
2423
2424				sub ceil ($) {
2425				require Math::AnyNum::ceil;
2426				my ($x) = @_;
2427
2428				if (ref($x) ne __PACKAGE__) {
2429				$x = __PACKAGE__->new($x);
2430				}
2431
2432				ref($$x) eq 'Math::GMPz' and return $x; # already an integer
2433				bless \__ceil__($$x);
2434				}
2435
2436				#
2437				## sin / sinh / asin / asinh
2438				#
2439
2440				sub sin { # used in overloading
2441				require Math::AnyNum::sin;
2442				bless \__sin__(_star2mpfr_mpc($_[0]));
2443				}
2444
2445				sub sinh ($) {
2446				require Math::AnyNum::sinh;
2447				bless \__sinh__(_star2mpfr_mpc($_[0]));
2448				}
2449
2450				sub asin ($) {
2451				require Math::AnyNum::asin;
2452				bless \__asin__(_star2mpfr_mpc($_[0]));
2453				}
2454
2455				sub asinh ($) {
2456				require Math::AnyNum::asinh;
2457				bless \__asinh__(_star2mpfr_mpc($_[0]));
2458				}
2459
2460				#
2461				## cos / cosh / acos / acosh
2462				#
2463
2464				sub cos { # used in overloading
2465				require Math::AnyNum::cos;
2466				bless \__cos__(_star2mpfr_mpc($_[0]));
2467				}
2468
2469				sub cosh ($) {
2470				require Math::AnyNum::cosh;
2471				bless \__cosh__(_star2mpfr_mpc($_[0]));
2472				}
2473
2474				sub acos ($) {
2475				require Math::AnyNum::acos;
2476				bless \__acos__(_star2mpfr_mpc($_[0]));
2477				}
2478
2479				sub acosh ($) {
2480				require Math::AnyNum::acosh;
2481				bless \__acosh__(_star2mpfr_mpc($_[0]));
2482				}
2483
2484				#
2485				## tan / tanh / atan / atanh
2486				#
2487
2488				sub tan ($) {
2489				require Math::AnyNum::tan;
2490				bless \__tan__(_star2mpfr_mpc($_[0]));
2491				}
2492
2493				sub tanh ($) {
2494				require Math::AnyNum::tanh;
2495				bless \__tanh__(_star2mpfr_mpc($_[0]));
2496				}
2497
2498				sub atan ($) {
2499				require Math::AnyNum::atan;
2500				bless \__atan__(_star2mpfr_mpc($_[0]));
2501				}
2502
2503				sub atanh ($) {
2504				require Math::AnyNum::atanh;
2505				bless \__atanh__(_star2mpfr_mpc($_[0]));
2506				}
2507
2508				sub atan2 ($$) {
2509				require Math::AnyNum::atan2;
2510				bless \__atan2__(_star2mpfr_mpc($_[0]), _star2mpfr_mpc($_[1]));
2511				}
2512
2513				#
2514				## sec / sech / asec / asech
2515				#
2516
2517				sub sec ($) {
2518				require Math::AnyNum::sec;
2519				bless \__sec__(_star2mpfr_mpc($_[0]));
2520				}
2521
2522				sub sech ($) {
2523				require Math::AnyNum::sech;
2524				bless \__sech__(_star2mpfr_mpc($_[0]));
2525				}
2526
2527				sub asec ($) {
2528				require Math::AnyNum::asec;
2529				bless \__asec__(_star2mpfr_mpc($_[0]));
2530				}
2531
2532				sub asech ($) {
2533				require Math::AnyNum::asech;
2534				bless \__asech__(_star2mpfr_mpc($_[0]));
2535				}
2536
2537				#
2538				## csc / csch / acsc / acsch
2539				#
2540
2541				sub csc ($) {
2542				require Math::AnyNum::csc;
2543				bless \__csc__(_star2mpfr_mpc($_[0]));
2544				}
2545
2546				sub csch ($) {
2547				require Math::AnyNum::csch;
2548				bless \__csch__(_star2mpfr_mpc($_[0]));
2549				}
2550
2551				sub acsc ($) {
2552				require Math::AnyNum::acsc;
2553				bless \__acsc__(_star2mpfr_mpc($_[0]));
2554				}
2555
2556				sub acsch ($) {
2557				require Math::AnyNum::acsch;
2558				bless \__acsch__(_star2mpfr_mpc($_[0]));
2559				}
2560
2561				#
2562				## cot / coth / acot / acoth
2563				#
2564
2565				sub cot ($) {
2566				require Math::AnyNum::cot;
2567				bless \__cot__(_star2mpfr_mpc($_[0]));
2568				}
2569
2570				sub coth ($) {
2571				require Math::AnyNum::coth;
2572				bless \__coth__(_star2mpfr_mpc($_[0]));
2573				}
2574
2575				sub acot ($) {
2576				require Math::AnyNum::acot;
2577				bless \__acot__(_star2mpfr_mpc($_[0]));
2578				}
2579
2580				sub acoth ($) {
2581				require Math::AnyNum::acoth;
2582				bless \__acoth__(_star2mpfr_mpc($_[0]));
2583				}
2584
2585				sub deg2rad ($) {
2586				require Math::AnyNum::mul;
2587				my ($x) = @_;
2588				my $f = Math::MPFR::Rmpfr_init2($PREC);
2589				Math::MPFR::Rmpfr_const_pi($f, $ROUND);
2590				Math::MPFR::Rmpfr_div_ui($f, $f, 180, $ROUND);
2591				bless \__mul__(_star2mpfr_mpc($x), $f);
2592				}
2593
2594				sub rad2deg ($) {
2595				require Math::AnyNum::mul;
2596				my ($x) = @_;
2597				my $f = Math::MPFR::Rmpfr_init2($PREC);
2598				Math::MPFR::Rmpfr_const_pi($f, $ROUND);
2599				Math::MPFR::Rmpfr_ui_div($f, 180, $f, $ROUND);
2600				bless \__mul__(_star2mpfr_mpc($x), $f);
2601				}
2602
2603				#
2604				## gamma
2605				#
2606
2607				sub gamma ($) {
2608				my $r = Math::MPFR::Rmpfr_init2($PREC);
2609				Math::MPFR::Rmpfr_gamma($r, _star2mpfr($_[0]), $ROUND);
2610				bless \$r;
2611				}
2612
2613				#
2614				## lgamma
2615				#
2616
2617				sub lgamma ($) {
2618				my $r = Math::MPFR::Rmpfr_init2($PREC);
2619				Math::MPFR::Rmpfr_lgamma($r, _star2mpfr($_[0]), $ROUND);
2620				bless \$r;
2621				}
2622
2623				#
2624				## lngamma
2625				#
2626
2627				sub lngamma ($) {
2628				my $r = Math::MPFR::Rmpfr_init2($PREC);
2629				Math::MPFR::Rmpfr_lngamma($r, _star2mpfr($_[0]), $ROUND);
2630				bless \$r;
2631				}
2632
2633				#
2634				## digamma
2635				#
2636
2637				sub digamma ($) {
2638				my $r = Math::MPFR::Rmpfr_init2($PREC);
2639				Math::MPFR::Rmpfr_digamma($r, _star2mpfr($_[0]), $ROUND);
2640				bless \$r;
2641				}
2642
2643				#
2644				## zeta
2645				#
2646
2647				sub zeta ($) {
2648				my ($x) = @_;
2649
2650				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
2651				## $x is an unsigned integer
2652				}
2653				else {
2654				$x = _star2mpfr($x);
2655
2656				# If $x fits inside an unsigned integer, then unpack it.
2657				if ( Math::MPFR::Rmpfr_integer_p($x)
2658				and Math::MPFR::Rmpfr_fits_ulong_p($x, $ROUND)) {
2659				$x = Math::MPFR::Rmpfr_get_ui($x, $ROUND);
2660				}
2661				}
2662
2663				my $r = Math::MPFR::Rmpfr_init2($PREC);
2664
2665				ref($x)
2666				? Math::MPFR::Rmpfr_zeta($r, $x, $ROUND)
2667				: Math::MPFR::Rmpfr_zeta_ui($r, $x, $ROUND);
2668
2669				bless \$r;
2670				}
2671
2672				#
2673				## eta
2674				#
2675
2676				sub eta ($) {
2677				require Math::AnyNum::eta;
2678				bless \__eta__(_star2mpfr($_[0]));
2679				}
2680
2681				#
2682				## beta
2683				#
2684				sub beta ($$) {
2685				require Math::AnyNum::beta;
2686				bless \__beta__(_star2mpfr($_[0]), _star2mpfr($_[1]));
2687				}
2688
2689				#
2690				## Airy function (Ai)
2691				#
2692
2693				sub Ai ($) {
2694				my $r = Math::MPFR::Rmpfr_init2($PREC);
2695				Math::MPFR::Rmpfr_ai($r, _star2mpfr($_[0]), $ROUND);
2696				bless \$r;
2697				}
2698
2699				#
2700				## Exponential integral (Ei)
2701				#
2702
2703				sub Ei ($) {
2704				my $r = Math::MPFR::Rmpfr_init2($PREC);
2705				Math::MPFR::Rmpfr_eint($r, _star2mpfr($_[0]), $ROUND);
2706				bless \$r;
2707				}
2708
2709				#
2710				## Logarithmic integral (Li)
2711				#
2712				sub Li ($) {
2713				my $r = Math::MPFR::Rmpfr_init2($PREC);
2714				Math::MPFR::Rmpfr_log($r, _star2mpfr($_[0]), $ROUND);
2715				Math::MPFR::Rmpfr_eint($r, $r, $ROUND);
2716				bless \$r;
2717				}
2718
2719				#
2720				## Dilogarithm function (Li_2)
2721				#
2722				sub Li2 ($) {
2723				my $r = Math::MPFR::Rmpfr_init2($PREC);
2724				Math::MPFR::Rmpfr_li2($r, _star2mpfr($_[0]), $ROUND);
2725				bless \$r;
2726				}
2727
2728				#
2729				## Error function
2730				#
2731				sub erf ($) {
2732				my $r = Math::MPFR::Rmpfr_init2($PREC);
2733				Math::MPFR::Rmpfr_erf($r, _star2mpfr($_[0]), $ROUND);
2734				bless \$r;
2735				}
2736
2737				#
2738				## Complementary error function
2739				#
2740				sub erfc ($) {
2741				my $r = Math::MPFR::Rmpfr_init2($PREC);
2742				Math::MPFR::Rmpfr_erfc($r, _star2mpfr($_[0]), $ROUND);
2743				bless \$r;
2744				}
2745
2746				#
2747				## Lambert W
2748				#
2749
2750				sub LambertW ($) {
2751				require Math::AnyNum::LambertW;
2752				bless \__LambertW__(_star2mpfr_mpc($_[0]));
2753				}
2754
2755				#
2756				## lgrt -- logarithmic root
2757				#
2758
2759				sub lgrt ($) {
2760				require Math::AnyNum::lgrt;
2761				bless \__lgrt__(_star2mpfr_mpc($_[0]));
2762				}
2763
2764				#
2765				## agm
2766				#
2767				sub agm ($$) {
2768				require Math::AnyNum::agm;
2769				bless \__agm__(_star2mpfr_mpc($_[0]), _star2mpfr_mpc($_[1]));
2770				}
2771
2772				#
2773				## hypot
2774				#
2775
2776				sub hypot ($$) {
2777				require Math::AnyNum::hypot;
2778				bless \__hypot__(_star2mpfr_mpc($_[0]), _star2mpfr_mpc($_[1]));
2779				}
2780
2781				#
2782				## BesselJ
2783				#
2784
2785				sub BesselJ ($$) {
2786				require Math::AnyNum::BesselJ;
2787				my ($x, $y) = @_;
2788
2789				$x = ref($x) eq __PACKAGE__ ? _any2mpfr($$x) : _star2mpfr($x);
2790
2791				if (!ref($y) and CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
2792				return bless \__BesselJ__($x, $y);
2793				}
2794
2795				bless \__BesselJ__($x, _star2mpz($y) // (goto &nan));
2796				}
2797
2798				#
2799				## BesselY
2800				#
2801
2802				sub BesselY ($$) {
2803				require Math::AnyNum::BesselY;
2804				my ($x, $y) = @_;
2805
2806				$x = ref($x) eq __PACKAGE__ ? _any2mpfr($$x) : _star2mpfr($x);
2807
2808				if (!ref($y) and CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
2809				return bless \__BesselY__($x, $y);
2810				}
2811
2812				bless \__BesselY__($x, _star2mpz($y) // (goto &nan));
2813				}
2814
2815				#
2816				## ROUND
2817				#
2818
2819				sub round ($;$) {
2820				require Math::AnyNum::round;
2821				my ($x, $y) = @_;
2822
2823				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
2824
2825				if (!defined($y)) {
2826				return bless \__round__($x, 0);
2827				}
2828
2829				if (!ref($y)) {
2830				if (CORE::int($y) eq $y and $y > LONG_MIN and $y < ULONG_MAX) {
2831				## `y` is a native integer
2832				}
2833				else {
2834				$y = _any2si(_str2obj($y)) // (goto &nan);
2835				}
2836				}
2837				elsif (ref($y) eq __PACKAGE__) {
2838				$y = _any2si($$y) // (goto &nan);
2839				}
2840				else {
2841				$y = _any2si(_star2obj($y)) // (goto &nan);
2842				}
2843
2844				bless \__round__($x, $y);
2845				}
2846
2847				#
2848				## RAND / IRAND
2849				#
2850
2851				{
2852				my $srand = srand();
2853
2854				{
2855				state $state = Math::MPFR::Rmpfr_randinit_mt_nobless();
2856				Math::MPFR::Rmpfr_randseed_ui($state, $srand);
2857
2858				sub rand (;$;$) {
2859				require Math::AnyNum::mul;
2860				my ($x, $y) = @_;
2861
2862				if (@_ == 0) {
2863				$x = one();
2864				}
2865
2866				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
2867
2868				if (!defined($y)) {
2869				my $rand = Math::MPFR::Rmpfr_init2($PREC);
2870				Math::MPFR::Rmpfr_urandom($rand, $state, $ROUND);
2871				return bless \__mul__($rand, $x);
2872				}
2873
2874				require Math::AnyNum::sub;
2875				require Math::AnyNum::add;
2876
2877				$y = ref($y) eq __PACKAGE__ ? $$y : _star2obj($y);
2878
2879				my $rand = Math::MPFR::Rmpfr_init2($PREC);
2880				Math::MPFR::Rmpfr_urandom($rand, $state, $ROUND);
2881				$rand = __mul__($rand, __sub__($y, $x));
2882				bless \__add__($rand, $x);
2883				}
2884
2885				sub seed ($) {
2886				my $z = _star2mpz($_[0]) // do {
2887				require Carp;
2888				Carp::croak("seed(): invalid seed value <<$_[0]>> (expected an integer)");
2889				};
2890				Math::MPFR::Rmpfr_randseed($state, $z);
2891				bless \$z;
2892				}
2893				}
2894
2895				{
2896				state $state = Math::GMPz::zgmp_randinit_mt_nobless();
2897				Math::GMPz::zgmp_randseed_ui($state, $srand);
2898
2899				sub irand ($;$) {
2900				require Math::AnyNum::irand;
2901				my ($x, $y) = @_;
2902
2903				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // (goto &nan);
2904
2905				if (!defined($y)) {
2906				return bless \__irand__($x, undef, $state);
2907				}
2908
2909				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // (goto &nan);
2910				bless \__irand__($x, $y, $state);
2911				}
2912
2913				sub iseed ($) {
2914				my $z = _star2mpz($_[0]) // do {
2915				require Carp;
2916				Carp::croak("iseed(): invalid seed value <<$_[0]>> (expected an integer)");
2917				};
2918				Math::GMPz::zgmp_randseed($state, $z);
2919				bless \$z;
2920				}
2921				}
2922				}
2923
2924				#
2925				## Fibonacci
2926				#
2927				sub fibonacci ($) {
2928				my ($x) = @_;
2929
2930				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
2931				## `x` is a native unsigned integer
2932				}
2933				elsif (ref($x) eq __PACKAGE__) {
2934				$x = _any2ui($$x) // goto &nan;
2935				}
2936				else {
2937				$x = _any2ui(_star2obj($x)) // goto &nan;
2938				}
2939
2940				my $r = Math::GMPz::Rmpz_init();
2941				Math::GMPz::Rmpz_fib_ui($r, $x);
2942				bless \$r;
2943				}
2944
2945				#
2946				## Lucas
2947				#
2948				sub lucas ($) {
2949				my ($x) = @_;
2950
2951				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
2952				## `x` is a native unsigned integer
2953				}
2954				elsif (ref($x) eq __PACKAGE__) {
2955				$x = _any2ui($$x) // goto &nan;
2956				}
2957				else {
2958				$x = _any2ui(_star2obj($x)) // goto &nan;
2959				}
2960
2961				my $r = Math::GMPz::Rmpz_init();
2962				Math::GMPz::Rmpz_lucnum_ui($r, $x);
2963				bless \$r;
2964				}
2965
2966				#
2967				## Primorial
2968				#
2969				sub primorial ($) {
2970				my ($x) = @_;
2971
2972				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
2973				## `x` is a native unsigned integer
2974				}
2975				elsif (ref($x) eq __PACKAGE__) {
2976				$x = _any2ui($$x) // goto &nan;
2977				}
2978				else {
2979				$x = _any2ui(_star2obj($x)) // goto &nan;
2980				}
2981
2982				my $r = Math::GMPz::Rmpz_init();
2983				Math::GMPz::Rmpz_primorial_ui($r, $x);
2984				bless \$r;
2985				}
2986
2987				#
2988				## bernfrac
2989				#
2990
2991				sub bernfrac ($) {
2992				require Math::AnyNum::bernfrac;
2993				my ($x) = @_;
2994
2995				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
2996				## `x` is a native unsigned integer
2997				}
2998				elsif (ref($x) eq __PACKAGE__) {
2999				$x = _any2ui($$x) // goto &nan;
3000				}
3001				else {
3002				$x = _any2ui(_star2obj($x)) // goto &nan;
3003				}
3004
3005				bless \__bernfrac__($x);
3006				}
3007
3008				#
3009				## harmfrac
3010				#
3011
3012				sub harmfrac ($) {
3013				require Math::AnyNum::harmfrac;
3014				my ($x) = @_;
3015
3016				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
3017				## `x` is a native unsigned integer
3018				}
3019				elsif (ref($x) eq __PACKAGE__) {
3020				$x = _any2ui($$x) // goto &nan;
3021				}
3022				else {
3023				$x = _any2ui(_star2obj($x)) // goto &nan;
3024				}
3025
3026				bless \__harmfrac__($x);
3027				}
3028
3029				#
3030				## bernreal
3031				#
3032
3033				sub bernreal ($) {
3034				require Math::AnyNum::bernreal;
3035				my ($x) = @_;
3036
3037				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
3038				## `x` is a native unsigned integer
3039				}
3040				elsif (ref($x) eq __PACKAGE__) {
3041				$x = _any2ui($$x) // goto &nan;
3042				}
3043				else {
3044				$x = _any2ui(_star2obj($x)) // goto &nan;
3045				}
3046
3047				bless \__bernreal__($x);
3048				}
3049
3050				#
3051				## harmreal
3052				#
3053
3054				sub harmreal ($) {
3055				require Math::AnyNum::harmreal;
3056				bless \__harmreal__(_star2mpfr($_[0]) // (goto &nan));
3057				}
3058
3059				#
3060				## Factorial
3061				#
3062				sub factorial ($) {
3063				my ($x) = @_;
3064
3065				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
3066				## `x` is a native unsigned integer
3067				}
3068				elsif (ref($x) eq __PACKAGE__) {
3069				$x = _any2ui($$x) // goto &nan;
3070				}
3071				else {
3072				$x = _any2ui(_star2obj($x)) // goto &nan;
3073				}
3074
3075				my $r = Math::GMPz::Rmpz_init();
3076				Math::GMPz::Rmpz_fac_ui($r, $x);
3077				bless \$r;
3078				}
3079
3080				#
3081				## Double-factorial
3082				#
3083
3084				sub dfactorial ($) {
3085				my ($x) = @_;
3086
3087				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
3088				## `x` is a native unsigned integer
3089				}
3090				elsif (ref($x) eq __PACKAGE__) {
3091				$x = _any2ui($$x) // goto &nan;
3092				}
3093				else {
3094				$x = _any2ui(_star2obj($x)) // goto &nan;
3095				}
3096
3097				my $r = Math::GMPz::Rmpz_init();
3098				Math::GMPz::Rmpz_2fac_ui($r, $x);
3099				bless \$r;
3100				}
3101
3102				#
3103				## M-factorial
3104				#
3105
3106				sub mfactorial ($$) {
3107				my ($x, $y) = @_;
3108
3109				if (!ref($x) and CORE::int($x) eq $x and $x >= 0 and $x < ULONG_MAX) {
3110				## `x` is an unsigned native integer
3111				}
3112				elsif (ref($x) eq __PACKAGE__) {
3113				$x = _any2ui($$x) // goto &nan;
3114				}
3115				else {
3116				$x = _any2ui(_star2obj($x)) // goto &nan;
3117				}
3118
3119				if (!ref($y) and CORE::int($y) eq $y and $y >= 0 and $y < ULONG_MAX) {
3120				## `y` is an unsigned native integer
3121				}
3122				elsif (ref($y) eq __PACKAGE__) {
3123				$y = _any2ui($$y) // goto &nan;
3124				}
3125				else {
3126				$y = _any2ui(_star2obj($y)) // goto &nan;
3127				}
3128
3129				my $r = Math::GMPz::Rmpz_init();
3130				Math::GMPz::Rmpz_mfac_uiui($r, $x, $y);
3131				bless \$r;
3132				}
3133
3134				#
3135				## falling_factorial(x, +y) = binomial(x, y) * y!
3136				## falling_factorial(x, -y) = 1/falling_factorial(x + y, y)
3137				#
3138				sub falling_factorial ($$) {
3139				my ($x, $y) = @_;
3140
3141				$x = _star2mpz($x) // goto &nan;
3142
3143				if (ref($y) eq __PACKAGE__) {
3144				$y = _any2si($$y) // goto &nan;
3145				}
3146				elsif (!ref($y) and CORE::int($y) eq $y and $y > LONG_MIN and $y < ULONG_MAX) {
3147				## `y` is a native integer
3148				}
3149				else {
3150				$y = _any2si(_star2obj($y)) // goto &nan;
3151				}
3152
3153				my $r = Math::GMPz::Rmpz_init_set($x);
3154
3155				if ($y < 0) {
3156				Math::GMPz::Rmpz_add_ui($r, $r, CORE::abs($y));
3157				}
3158
3159				Math::GMPz::Rmpz_fits_ulong_p($r)
3160				? Math::GMPz::Rmpz_bin_uiui($r, Math::GMPz::Rmpz_get_ui($r), CORE::abs($y))
3161				: Math::GMPz::Rmpz_bin_ui($r, $r, CORE::abs($y));
3162
3163				Math::GMPz::Rmpz_sgn($r) \|\| do {
3164				$y < 0
3165				? (goto &nan)
3166				: (goto &zero);
3167				};
3168
3169				state $t = Math::GMPz::Rmpz_init_nobless();
3170				Math::GMPz::Rmpz_fac_ui($t, CORE::abs($y));
3171				Math::GMPz::Rmpz_mul($r, $r, $t);
3172
3173				if ($y < 0) {
3174				my $q = Math::GMPq::Rmpq_init();
3175				Math::GMPq::Rmpq_set_z($q, $r);
3176				Math::GMPq::Rmpq_inv($q, $q);
3177				return bless \$q;
3178				}
3179
3180				bless \$r;
3181				}
3182
3183				#
3184				## rising_factorial(x, +y) = binomial(x + y - 1, y) * y!
3185				## rising_factorial(x, -y) = 1/rising_factorial(x - y, y)
3186				#
3187				sub rising_factorial ($$) {
3188				my ($x, $y) = @_;
3189
3190				$x = _star2mpz($x) // goto &nan;
3191
3192				if (ref($y) eq __PACKAGE__) {
3193				$y = _any2si($$y) // goto &nan;
3194				}
3195				elsif (!ref($y) and CORE::int($y) eq $y and $y > LONG_MIN and $y < ULONG_MAX) {
3196				## `y` is a native integer
3197				}
3198				else {
3199				$y = _any2si(_star2obj($y)) // goto &nan;
3200				}
3201
3202				my $r = Math::GMPz::Rmpz_init_set($x);
3203				Math::GMPz::Rmpz_add_ui($r, $r, CORE::abs($y));
3204				Math::GMPz::Rmpz_sub_ui($r, $r, 1);
3205
3206				if ($y < 0) {
3207				Math::GMPz::Rmpz_sub_ui($r, $r, CORE::abs($y));
3208				}
3209
3210				Math::GMPz::Rmpz_fits_ulong_p($r)
3211				? Math::GMPz::Rmpz_bin_uiui($r, Math::GMPz::Rmpz_get_ui($r), CORE::abs($y))
3212				: Math::GMPz::Rmpz_bin_ui($r, $r, CORE::abs($y));
3213
3214				Math::GMPz::Rmpz_sgn($r) \|\| do {
3215				$y < 0
3216				? (goto &nan)
3217				: (goto &zero);
3218				};
3219
3220				state $t = Math::GMPz::Rmpz_init_nobless();
3221				Math::GMPz::Rmpz_fac_ui($t, CORE::abs($y));
3222				Math::GMPz::Rmpz_mul($r, $r, $t);
3223
3224				if ($y < 0) {
3225				my $q = Math::GMPq::Rmpq_init();
3226				Math::GMPq::Rmpq_set_z($q, $r);
3227				Math::GMPq::Rmpq_inv($q, $q);
3228				return bless \$q;
3229				}
3230
3231				bless \$r;
3232				}
3233
3234				#
3235				## Greatest common multiple
3236				#
3237
3238				sub gcd ($$) {
3239				my ($x, $y) = @_;
3240
3241				if (ref($y) and !ref($x)) {
3242				($x, $y) = ($y, $x);
3243				}
3244
3245				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // (goto &nan);
3246
3247				my $r = Math::GMPz::Rmpz_init();
3248
3249				if (!ref($y) and CORE::int($y) eq $y and CORE::abs($y) < ULONG_MAX) {
3250				Math::GMPz::Rmpz_gcd_ui($r, $x, CORE::abs($y));
3251				}
3252				else {
3253				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // (goto &nan);
3254				Math::GMPz::Rmpz_gcd($r, $x, $y);
3255				}
3256
3257				bless \$r;
3258				}
3259
3260				#
3261				## Least common multiple
3262				#
3263
3264				sub lcm ($$) {
3265				my ($x, $y) = @_;
3266
3267				if (ref($y) and !ref($x)) {
3268				($x, $y) = ($y, $x);
3269				}
3270
3271				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // (goto &nan);
3272
3273				my $r = Math::GMPz::Rmpz_init();
3274
3275				if (!ref($y) and CORE::int($y) eq $y and CORE::abs($y) < ULONG_MAX) {
3276				Math::GMPz::Rmpz_lcm_ui($r, $x, CORE::abs($y));
3277				}
3278				else {
3279				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // (goto &nan);
3280				Math::GMPz::Rmpz_lcm($r, $x, $y);
3281				}
3282
3283				bless \$r;
3284				}
3285
3286				#
3287				## Next prime after `x`.
3288				#
3289
3290				sub next_prime ($) {
3291				my ($x) = @_;
3292				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
3293				my $r = Math::GMPz::Rmpz_init();
3294				Math::GMPz::Rmpz_nextprime($r, $x);
3295				bless \$r;
3296				}
3297
3298				#
3299				## Is prime?
3300				#
3301
3302				sub is_prime ($;$) {
3303				require Math::AnyNum::is_int;
3304				my ($x, $y) = @_;
3305
3306				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3307
3308				__is_int__($x) \|\| return 0;
3309
3310				$y = defined($y) ? (CORE::abs(CORE::int($y)) \|\| 20) : 20;
3311				Math::GMPz::Rmpz_probab_prime_p(_any2mpz($x) // (return 0), $y);
3312				}
3313
3314				#
3315				## Is `x` coprime to `y`?
3316				#
3317
3318				sub is_coprime ($$) {
3319				require Math::AnyNum::is_int;
3320				my ($x, $y) = @_;
3321
3322				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3323
3324				__is_int__($x) \|\| return 0;
3325
3326				$x = _any2mpz($x) // return 0;
3327
3328				if (!ref($y) and CORE::int($y) eq $y and $y >= 0 and $y < ULONG_MAX) {
3329				## `y` is a native integer
3330				}
3331				else {
3332				$y = ref($y) eq __PACKAGE__ ? $$y : _star2obj($y);
3333				__is_int__($y) \|\| return 0;
3334				$y = _any2mpz($y) // return 0;
3335				}
3336
3337				state $t = Math::GMPz::Rmpz_init_nobless();
3338
3339				ref($y)
3340				? Math::GMPz::Rmpz_gcd($t, $x, $y)
3341				: Math::GMPz::Rmpz_gcd_ui($t, $x, $y);
3342
3343				Math::GMPz::Rmpz_cmp_ui($t, 1) == 0;
3344				}
3345
3346				#
3347				## Is integer?
3348				#
3349
3350				sub is_int ($) {
3351				require Math::AnyNum::is_int;
3352				my ($x) = @_;
3353				__is_int__(ref($x) eq __PACKAGE__ ? $$x : _star2obj($x));
3354				}
3355
3356				#
3357				## Is rational?
3358				#
3359
3360				sub is_rat ($) {
3361				my ($x) = @_;
3362				my $ref = ref(ref($x) eq __PACKAGE__ ? $$x : _star2obj($x));
3363				$ref eq 'Math::GMPz' or $ref eq 'Math::GMPq';
3364				}
3365
3366				#
3367				## Numerator of a number
3368				#
3369
3370				sub numerator ($) {
3371				my ($x) = @_;
3372
3373				my $r = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3374
3375				while (1) {
3376
3377				if (ref($r) eq 'Math::GMPq') {
3378				my $z = Math::GMPz::Rmpz_init();
3379				Math::GMPq::Rmpq_get_num($z, $r);
3380				return bless \$z;
3381				}
3382
3383				ref($r) eq 'Math::GMPz' and return $x; # is an integer
3384
3385				$r = _any2mpq($r) // goto &nan;
3386				}
3387				}
3388
3389				#
3390				## Denominator of a number
3391				#
3392
3393				sub denominator ($) {
3394				my ($x) = @_;
3395
3396				my $r = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3397
3398				while (1) {
3399
3400				if (ref($r) eq 'Math::GMPq') {
3401				my $z = Math::GMPz::Rmpz_init();
3402				Math::GMPq::Rmpq_get_den($z, $r);
3403				return bless \$z;
3404				}
3405
3406				ref($r) eq 'Math::GMPz' and goto &one; # is an integer
3407
3408				$r = _any2mpq($r) // goto &nan;
3409				}
3410				}
3411
3412				#
3413				## (numerator, denominator)
3414				#
3415
3416				sub nude ($) {
3417				my ($x) = @_;
3418
3419				if (ref($x) ne __PACKAGE__) {
3420				$x = __PACKAGE__->new($x);
3421				}
3422
3423				($x->numerator, $x->denominator);
3424				}
3425
3426				#
3427				## Sign of a number
3428				#
3429
3430				sub sgn ($) {
3431				require Math::AnyNum::sgn;
3432				my ($x) = @_;
3433				my $r = __sgn__(ref($x) eq __PACKAGE__ ? $$x : _star2obj($x));
3434				ref($r) ? (bless \$r) : $r;
3435				}
3436
3437				#
3438				## Is a real number?
3439				#
3440
3441				sub is_real ($) {
3442				my ($x) = @_;
3443
3444				my $r = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3445
3446				while (1) {
3447				my $ref = ref($r);
3448
3449				$ref eq 'Math::GMPz' && return 1;
3450				$ref eq 'Math::GMPq' && return 1;
3451				$ref eq 'Math::MPFR' && return Math::MPFR::Rmpfr_number_p($r);
3452
3453				$r = _any2mpfr($r);
3454				}
3455				}
3456
3457				#
3458				## Is an imaginary number?
3459				#
3460
3461				sub is_imag ($) {
3462				my ($x) = @_;
3463
3464				my $r = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3465				ref($r) eq 'Math::MPC' or return 0;
3466
3467				my $f = Math::MPFR::Rmpfr_init2($PREC);
3468				Math::MPC::RMPC_RE($f, $r);
3469				Math::MPFR::Rmpfr_zero_p($f) \|\| return 0; # is complex
3470				Math::MPC::RMPC_IM($f, $r);
3471				!Math::MPFR::Rmpfr_zero_p($f);
3472				}
3473
3474				#
3475				## Is a complex number?
3476				#
3477
3478				sub is_complex ($) {
3479				my ($x) = @_;
3480
3481				my $r = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3482				ref($r) eq 'Math::MPC' or return 0;
3483
3484				my $f = Math::MPFR::Rmpfr_init2($PREC);
3485				Math::MPC::RMPC_IM($f, $r);
3486				Math::MPFR::Rmpfr_zero_p($f) && return 0; # is real
3487				Math::MPC::RMPC_RE($f, $r);
3488				!Math::MPFR::Rmpfr_zero_p($f);
3489				}
3490
3491				#
3492				## Is positive infinity?
3493				#
3494
3495				sub is_inf ($) {
3496				my ($x) = @_;
3497
3498				my $r = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3499
3500				while (1) {
3501				my $ref = ref($r);
3502
3503				$ref eq 'Math::GMPz' && return 0;
3504				$ref eq 'Math::GMPq' && return 0;
3505				$ref eq 'Math::MPFR' && return (Math::MPFR::Rmpfr_inf_p($r) and Math::MPFR::Rmpfr_sgn($r) > 0);
3506
3507				$r = _any2mpfr($r);
3508				}
3509				}
3510
3511				#
3512				## Is negative infinity?
3513				#
3514
3515				sub is_ninf ($) {
3516				my ($x) = @_;
3517
3518				my $r = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3519
3520				while (1) {
3521				my $ref = ref($r);
3522
3523				$ref eq 'Math::GMPz' && return 0;
3524				$ref eq 'Math::GMPq' && return 0;
3525				$ref eq 'Math::MPFR' && return (Math::MPFR::Rmpfr_inf_p($r) and Math::MPFR::Rmpfr_sgn($r) < 0);
3526
3527				$r = _any2mpfr($r);
3528				}
3529				}
3530
3531				#
3532				## Is Not-A-Number?
3533				#
3534
3535				sub is_nan ($) {
3536				my ($x) = @_;
3537
3538				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3539
3540				ref($x) eq 'Math::GMPz' && return 0;
3541				ref($x) eq 'Math::GMPq' && return 0;
3542				ref($x) eq 'Math::MPFR' && return Math::MPFR::Rmpfr_nan_p($x);
3543
3544				my $t = Math::MPFR::Rmpfr_init2($PREC);
3545
3546				Math::MPC::RMPC_RE($t, $x);
3547				Math::MPFR::Rmpfr_nan_p($t) && return 1;
3548
3549				Math::MPC::RMPC_IM($t, $x);
3550				Math::MPFR::Rmpfr_nan_p($t) && return 1;
3551
3552				return 0;
3553				}
3554
3555				#
3556				## Is an even integer?
3557				#
3558
3559				sub is_even ($) {
3560				require Math::AnyNum::is_int;
3561				my ($x) = @_;
3562
3563				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3564
3565				__is_int__($x)
3566				&& Math::GMPz::Rmpz_even_p(_any2mpz($x) // (return 0));
3567				}
3568
3569				#
3570				## Is an odd integer?
3571				#
3572
3573				sub is_odd ($) {
3574				require Math::AnyNum::is_int;
3575				my ($x) = @_;
3576
3577				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3578
3579				__is_int__($x)
3580				&& Math::GMPz::Rmpz_odd_p(_any2mpz($x) // (return 0));
3581				}
3582
3583				#
3584				## Is zero?
3585				#
3586
3587				sub is_zero ($) {
3588				require Math::AnyNum::eq;
3589				my ($x) = @_;
3590				(@_) = ((ref($x) eq __PACKAGE__ ? $$x : _star2obj($x)), 0);
3591				goto &__eq__;
3592				}
3593
3594				#
3595				## Is one?
3596				#
3597
3598				sub is_one ($) {
3599				require Math::AnyNum::eq;
3600				my ($x) = @_;
3601				(@_) = ((ref($x) eq __PACKAGE__ ? $$x : _star2obj($x)), 1);
3602				goto &__eq__;
3603				}
3604
3605				#
3606				## Is minus one?
3607				#
3608
3609				sub is_mone ($) {
3610				require Math::AnyNum::eq;
3611				my ($x) = @_;
3612				(@_) = ((ref($x) eq __PACKAGE__ ? $$x : _star2obj($x)), -1);
3613				goto &__eq__;
3614				}
3615
3616				#
3617				## Is positive?
3618				#
3619
3620				sub is_pos ($) {
3621				require Math::AnyNum::cmp;
3622				my ($x) = @_;
3623				(__cmp__((ref($x) eq __PACKAGE__ ? $$x : _star2obj($x)), 0) // return undef) > 0;
3624				}
3625
3626				#
3627				## Is negative?
3628				#
3629
3630				sub is_neg ($) {
3631				require Math::AnyNum::cmp;
3632				my ($x) = @_;
3633				(__cmp__((ref($x) eq __PACKAGE__ ? $$x : _star2obj($x)), 0) // return undef) < 0;
3634				}
3635
3636				#
3637				## Is square?
3638				#
3639
3640				sub is_square ($) {
3641				require Math::AnyNum::is_int;
3642				my ($x, $y) = @_;
3643
3644				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3645
3646				__is_int__($x)
3647				&& Math::GMPz::Rmpz_perfect_square_p(_any2mpz($x) // (return 0));
3648				}
3649
3650				#
3651				## Is a polygonal number?
3652				#
3653
3654				sub is_polygonal ($$) {
3655				require Math::AnyNum::is_int;
3656				require Math::AnyNum::is_polygonal;
3657				my ($n, $k) = @_;
3658
3659				$n = ref($n) eq __PACKAGE__ ? $$n : _star2obj($n);
3660
3661				$n = (__is_int__($n) ? _any2mpz($n) : return 0) // return 0;
3662				$k = (ref($k) eq __PACKAGE__ ? _any2mpz($$k) : _star2mpz($k)) // return 0;
3663
3664				__is_polygonal__($n, $k);
3665				}
3666
3667				#
3668				## Is a second polygonal number?
3669				#
3670
3671				sub is_polygonal2 ($$) {
3672				require Math::AnyNum::is_int;
3673				require Math::AnyNum::is_polygonal;
3674				my ($n, $k) = @_;
3675
3676				$n = ref($n) eq __PACKAGE__ ? $$n : _star2obj($n);
3677
3678				$n = (__is_int__($n) ? _any2mpz($n) : return 0) // return 0;
3679				$k = (ref($k) eq __PACKAGE__ ? _any2mpz($$k) : _star2mpz($k)) // return 0;
3680
3681				__is_polygonal__($n, $k, 1);
3682				}
3683
3684				#
3685				## Integer polygonal root
3686				#
3687
3688				sub ipolygonal_root ($$) {
3689				require Math::AnyNum::ipolygonal_root;
3690				my ($n, $k) = @_;
3691
3692				$n = (ref($n) eq __PACKAGE__ ? _any2mpz($$n) : _star2mpz($n)) // goto &nan;
3693				$k = (ref($k) eq __PACKAGE__ ? _any2mpz($$k) : _star2mpz($k)) // goto &nan;
3694
3695				bless \__ipolygonal_root__($n, $k);
3696				}
3697
3698				#
3699				## Second integer polygonal root
3700				#
3701
3702				sub ipolygonal_root2 ($$) {
3703				require Math::AnyNum::ipolygonal_root;
3704				my ($n, $k) = @_;
3705
3706				$n = (ref($n) eq __PACKAGE__ ? _any2mpz($$n) : _star2mpz($n)) // goto &nan;
3707				$k = (ref($k) eq __PACKAGE__ ? _any2mpz($$k) : _star2mpz($k)) // goto &nan;
3708
3709				bless \__ipolygonal_root__($n, $k, 1);
3710				}
3711
3712				#
3713				## n-th k-gonal number
3714				#
3715
3716				sub polygonal ($$) {
3717				my ($n, $k) = @_;
3718
3719				$n = (ref($n) eq __PACKAGE__ ? _any2mpz($$n) : _star2mpz($n)) // goto &nan;
3720
3721				if (!ref($k) and CORE::int($k) eq $k and $k >= 0 and $k < ULONG_MAX) {
3722				## `k` is a native unsigned integer
3723				}
3724				else {
3725				$k = (ref($k) eq __PACKAGE__ ? _any2mpz($$k) : _star2mpz($k)) // goto &nan;
3726				}
3727
3728				#
3729				## polygonal(n, k) = n * (kn - k - 2n + 4) / 2
3730				#
3731
3732				my $r = Math::GMPz::Rmpz_init();
3733
3734				if (!ref($k)) { # `k` is a native unsigned integer
3735				Math::GMPz::Rmpz_mul_ui($r, $n, $k); # r = n*k
3736				Math::GMPz::Rmpz_sub_ui($r, $r, $k); # r = r-k
3737				}
3738				else {
3739				Math::GMPz::Rmpz_mul($r, $n, $k); # r = n*k
3740				Math::GMPz::Rmpz_sub($r, $r, $k); # r = r-k
3741				}
3742
3743				Math::GMPz::Rmpz_submul_ui($r, $n, 2); # r = r-2*n
3744				Math::GMPz::Rmpz_add_ui($r, $r, 4); # r = r+4
3745				Math::GMPz::Rmpz_mul($r, $r, $n); # r = r*n
3746				Math::GMPz::Rmpz_div_2exp($r, $r, 1); # r = r/2
3747
3748				bless \$r;
3749				}
3750
3751				#
3752				## is_power
3753				#
3754
3755				sub is_power ($;$) {
3756				require Math::AnyNum::is_power;
3757				require Math::AnyNum::is_int;
3758				my ($x, $y) = @_;
3759
3760				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
3761
3762				__is_int__($x) \|\| return 0;
3763				$x = _any2mpz($x) // goto &nan;
3764
3765				if (!defined($y)) {
3766				return Math::GMPz::Rmpz_perfect_power_p($x);
3767				}
3768
3769				if (!ref($y) and CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
3770				## `y` is a native integer
3771				}
3772				else {
3773				$y = _any2si(ref($y) eq __PACKAGE__ ? $$y : _star2obj($y)) // return 0;
3774				}
3775
3776				__is_power__($x, $y);
3777				}
3778
3779				#
3780				## kronecker
3781				#
3782
3783				sub kronecker ($$) {
3784				my ($x, $y) = @_;
3785
3786				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
3787
3788				if (!ref($y) and CORE::int($y) eq $y and $y < ULONG_MAX and $y > LONG_MIN) {
3789				return (
3790				$y < 0
3791				? Math::GMPz::Rmpz_kronecker_si($x, $y)
3792				: Math::GMPz::Rmpz_kronecker_ui($x, $y)
3793				);
3794				}
3795
3796				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // goto &nan;
3797
3798				Math::GMPz::Rmpz_kronecker($x, $y);
3799				}
3800
3801				#
3802				## valuation
3803				#
3804
3805				sub valuation ($$) {
3806				require Math::AnyNum::valuation;
3807				my ($x, $y) = @_;
3808
3809				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
3810				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // goto &nan;
3811
3812				(__valuation__($x, $y))[0];
3813				}
3814
3815				#
3816				## remdiv
3817				#
3818
3819				sub remdiv ($$) {
3820				require Math::AnyNum::valuation;
3821				my ($x, $y) = @_;
3822
3823				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
3824				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // goto &nan;
3825
3826				bless \((__valuation__($x, $y))[1]);
3827				}
3828
3829				#
3830				## Invmod
3831				#
3832
3833				sub invmod ($$) {
3834				my ($x, $y) = @_;
3835
3836				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
3837				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // goto &nan;
3838
3839				my $r = Math::GMPz::Rmpz_init();
3840				Math::GMPz::Rmpz_invert($r, $x, $y) \|\| (goto &nan);
3841				bless \$r;
3842				}
3843
3844				#
3845				## Powmod
3846				#
3847
3848				sub powmod ($$$) {
3849				my ($x, $y, $z) = @_;
3850
3851				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
3852				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // goto &nan;
3853				$z = (ref($z) eq __PACKAGE__ ? _any2mpz($$z) : _star2mpz($z)) // goto &nan;
3854
3855				Math::GMPz::Rmpz_sgn($z) \|\| goto &nan;
3856
3857				if (Math::GMPz::Rmpz_sgn($y) < 0) {
3858				my $t = Math::GMPz::Rmpz_init();
3859				Math::GMPz::Rmpz_gcd($t, $x, $z);
3860				Math::GMPz::Rmpz_cmp_ui($t, 1) == 0 or goto &nan;
3861				}
3862
3863				my $r = Math::GMPz::Rmpz_init();
3864				Math::GMPz::Rmpz_powm($r, $x, $y, $z);
3865				bless \$r;
3866				}
3867
3868				#
3869				## Faulhaber summation formula
3870				#
3871
3872				sub faulhaber_sum ($$) {
3873				require Math::AnyNum::bernfrac;
3874				my ($n, $p) = @_;
3875
3876				my $native_n = 0; # true when `n` is a native integer
3877
3878				if (!ref($n) and CORE::int($n) eq $n and $n >= 0 and $n < ULONG_MAX) {
3879				## `n` is a native unsigned integer
3880				$native_n = 1;
3881				}
3882				else {
3883				$n = (ref($n) eq __PACKAGE__ ? _any2mpz($$n) : _star2mpz($n)) // goto &nan;
3884
3885				# Try to unbox `n` when it fits inside a native unsigned integer
3886				if (Math::GMPz::Rmpz_fits_ulong_p($n)) {
3887				$native_n = 1;
3888				$n = Math::GMPz::Rmpz_get_ui($n);
3889				}
3890				}
3891
3892				if (!ref($p) and CORE::int($p) eq $p and $p >= 0 and $p < ULONG_MAX) {
3893				## `p` is already a native unsigned integer
3894				}
3895				else {
3896				$p = (ref($p) eq __PACKAGE__ ? _any2ui($$p) : _any2ui(_star2obj($p))) // goto &nan;
3897				}
3898
3899				state @cache; # cache for Bernoulli numbers
3900
3901				my $t = Math::GMPz::Rmpz_init();
3902				my $u = Math::GMPz::Rmpz_init();
3903
3904				my $numerator = Math::GMPz::Rmpz_init();
3905				my $denominator = Math::GMPz::Rmpz_init_set_ui(1);
3906
3907				#<<<
3908				$native_n
3909				? Math::GMPz::Rmpz_ui_pow_ui($numerator, $n, $p + 1) # numerator = n^(p + 1)
3910				: Math::GMPz::Rmpz_pow_ui( $numerator, $n, $p + 1); # ==//==
3911				#>>>
3912
3913				foreach my $j (1 .. $p) {
3914
3915				# When `j` is odd and greater than 1, we can skip it.
3916				$j % 2 == 0 or $j == 1 or next;
3917
3918				Math::GMPz::Rmpz_bin_uiui($t, $p + 1, $j); # t = binomial(p+1, j)
3919
3920				#<<<
3921				$native_n
3922				? Math::GMPz::Rmpz_ui_pow_ui($u, $n, $p + 1 - $j) # u = n^(p + 1 - j)
3923				: Math::GMPz::Rmpz_pow_ui( $u, $n, $p + 1 - $j); # ==//==
3924				#>>>
3925
3926				# Compute Bernouli(j)
3927				my $bern = ($j <= 100 ? ($cache[$j] //= __bernfrac__($j)) : __bernfrac__($j));
3928
3929				#<<<
3930				Math::GMPz::Rmpz_mul($t, $t, $u); # t = t * u
3931				Math::GMPq::Rmpq_get_num($u, $bern); # u = numerator(bern)
3932				Math::GMPz::Rmpz_mul($t, $t, $u); # t = t * u
3933				Math::GMPq::Rmpq_get_den($u, $bern); # u = denominator(bern)
3934
3935				Math::GMPz::Rmpz_mul( $numerator, $numerator, $u); # numerator = numerator * u
3936				Math::GMPz::Rmpz_addmul($numerator, $denominator, $t); # numerator += denominator * t
3937				Math::GMPz::Rmpz_mul( $denominator, $denominator, $u); # denominator = denominator * u
3938				#>>>
3939				}
3940
3941				#<<<
3942				Math::GMPz::Rmpz_mul_ui($denominator, $denominator, $p + 1); # denominator = denominator * (p+1)
3943				Math::GMPz::Rmpz_divexact($numerator, $numerator, $denominator); # numerator = numerator / denominator
3944				#>>>
3945
3946				bless \$numerator;
3947				}
3948
3949				#
3950				## Binomial
3951				#
3952
3953				sub binomial ($$) {
3954				my ($x, $y) = @_;
3955
3956				# `x` and `y` are native unsigned integers
3957				if ( !ref($x)
3958				and !ref($y)
3959				and CORE::int($x) eq $x
3960				and CORE::int($y) eq $y
3961				and $x >= 0
3962				and $y >= 0
3963				and $x < ULONG_MAX
3964				and $y < ULONG_MAX) {
3965				my $r = Math::GMPz::Rmpz_init();
3966				Math::GMPz::Rmpz_bin_uiui($r, $x, $y);
3967				return bless \$r;
3968				}
3969
3970				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
3971
3972				if (!ref($y) and CORE::int($y) eq $y and $y > LONG_MIN and $y < ULONG_MAX) {
3973				## `y` is a native integer
3974				}
3975				else {
3976				$y = _any2si(ref($y) eq __PACKAGE__ ? $$y : _star2obj($y)) // goto &nan;
3977				}
3978
3979				my $r = Math::GMPz::Rmpz_init();
3980
3981				if ($y >= 0 and Math::GMPz::Rmpz_fits_ulong_p($x)) {
3982				Math::GMPz::Rmpz_bin_uiui($r, Math::GMPz::Rmpz_get_ui($x), $y);
3983				}
3984				else {
3985				$y < 0
3986				? Math::GMPz::Rmpz_bin_si($r, $x, $y)
3987				: Math::GMPz::Rmpz_bin_ui($r, $x, $y);
3988				}
3989
3990				bless \$r;
3991				}
3992
3993				#
3994				## AND
3995				#
3996
3997				sub and { # used in overloading
3998				my ($x, $y) = @_;
3999
4000				$x = _any2mpz($$x) // (goto &nan);
4001				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // (goto &nan);
4002
4003				my $r = Math::GMPz::Rmpz_init();
4004				Math::GMPz::Rmpz_and($r, $x, $y);
4005				bless \$r;
4006				}
4007
4008				#
4009				## OR
4010				#
4011
4012				sub or { # used in overloading
4013				my ($x, $y) = @_;
4014
4015				$x = _any2mpz($$x) // (goto &nan);
4016				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // (goto &nan);
4017
4018				my $r = Math::GMPz::Rmpz_init();
4019				Math::GMPz::Rmpz_ior($r, $x, $y);
4020				bless \$r;
4021				}
4022
4023				#
4024				## XOR
4025				#
4026
4027				sub xor { # used in overloading
4028				my ($x, $y) = @_;
4029
4030				$x = _any2mpz($$x) // (goto &nan);
4031				$y = (ref($y) eq __PACKAGE__ ? _any2mpz($$y) : _star2mpz($y)) // (goto &nan);
4032
4033				my $r = Math::GMPz::Rmpz_init();
4034				Math::GMPz::Rmpz_xor($r, $x, $y);
4035				bless \$r;
4036				}
4037
4038				#
4039				## NOT
4040				#
4041
4042				sub not { # used in overloading
4043				my ($x) = @_;
4044				$x = _any2mpz($$x) // (goto &nan);
4045				my $r = Math::GMPz::Rmpz_init();
4046				Math::GMPz::Rmpz_com($r, $x);
4047				bless \$r;
4048				}
4049
4050				#
4051				## LEFT SHIFT
4052				#
4053
4054				sub lsft { # used in overloading
4055				my ($x, $y) = @_;
4056
4057				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
4058
4059				if (!ref($y) and CORE::int($y) eq $y and $y > LONG_MIN and $y < ULONG_MAX) {
4060				## `y` is a native integer
4061				}
4062				else {
4063				$y = (ref($y) eq __PACKAGE__ ? _any2si($$y) : _any2si(_star2obj($y))) // goto &nan;
4064				}
4065
4066				my $r = Math::GMPz::Rmpz_init();
4067
4068				$y < 0
4069				? Math::GMPz::Rmpz_div_2exp($r, $x, -$y)
4070				: Math::GMPz::Rmpz_mul_2exp($r, $x, $y);
4071
4072				bless \$r;
4073				}
4074
4075				#
4076				## RIGHT SHIFT
4077				#
4078
4079				sub rsft { # used in overloading
4080				my ($x, $y) = @_;
4081
4082				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _star2mpz($x)) // goto &nan;
4083
4084				if (!ref($y) and CORE::int($y) eq $y and $y > LONG_MIN and $y < ULONG_MAX) {
4085				## `y` is a native integer
4086				}
4087				else {
4088				$y = (ref($y) eq __PACKAGE__ ? _any2si($$y) : _any2si(_star2obj($y))) // goto &nan;
4089				}
4090
4091				my $r = Math::GMPz::Rmpz_init();
4092
4093				$y < 0
4094				? Math::GMPz::Rmpz_mul_2exp($r, $x, -$y)
4095				: Math::GMPz::Rmpz_div_2exp($r, $x, $y);
4096
4097				bless \$r;
4098				}
4099
4100				#
4101				## POPCOUNT
4102				#
4103
4104				sub popcount ($) {
4105				my ($x) = @_;
4106
4107				$x = (ref($x) eq __PACKAGE__ ? _any2mpz($$x) : _any2mpz(_star2obj($x))) // return -1;
4108
4109				if (Math::GMPz::Rmpz_sgn($x) < 0) {
4110				my $t = Math::GMPz::Rmpz_init();
4111				Math::GMPz::Rmpz_neg($t, $x);
4112				$x = $t;
4113				}
4114
4115				Math::GMPz::Rmpz_popcount($x);
4116				}
4117
4118				#
4119				## Conversions
4120				#
4121
4122				sub as_bin ($) {
4123				Math::GMPz::Rmpz_get_str((_star2mpz($_[0]) // return undef), 2);
4124				}
4125
4126				sub as_oct ($) {
4127				Math::GMPz::Rmpz_get_str((_star2mpz($_[0]) // return undef), 8);
4128				}
4129
4130				sub as_hex ($) {
4131				Math::GMPz::Rmpz_get_str((_star2mpz($_[0]) // return undef), 16);
4132				}
4133
4134				sub as_int ($;$) {
4135				my ($x, $y) = @_;
4136
4137				my $base = 10;
4138				if (defined($y)) {
4139
4140				if (!ref($y) and CORE::int($y) eq $y) {
4141				$base = $y;
4142				}
4143				elsif (ref($y) eq __PACKAGE__) {
4144				$base = _any2ui($$y) // 0;
4145				}
4146				else {
4147				$base = _any2ui(_star2mpz($y) // return undef) // 0;
4148				}
4149
4150				if ($base < 2 or $base > 36) {
4151				require Carp;
4152				Carp::croak("base must be between 2 and 36, got $y");
4153				}
4154				}
4155
4156				Math::GMPz::Rmpz_get_str((_star2mpz($x) // return undef), $base);
4157				}
4158
4159				sub as_frac ($;$) {
4160				my ($x, $y) = @_;
4161
4162				my $base = 10;
4163				if (defined($y)) {
4164
4165				if (!ref($y) and CORE::int($y) eq $y) {
4166				$base = $y;
4167				}
4168				elsif (ref($y) eq __PACKAGE__) {
4169				$base = _any2ui($$y) // 0;
4170				}
4171				else {
4172				$base = _any2ui(_star2mpz($y) // return undef) // 0;
4173				}
4174
4175				if ($base < 2 or $base > 36) {
4176				require Carp;
4177				Carp::croak("base must be between 2 and 36, got $y");
4178				}
4179				}
4180
4181				$x = ref($x) eq __PACKAGE__ ? $$x : _star2obj($x);
4182
4183				my $ref = ref($x);
4184				if ( $ref eq 'Math::GMPq'
4185				or $ref eq 'Math::GMPz') {
4186				my $frac = (
4187				$ref eq 'Math::GMPq'
4188				? Math::GMPq::Rmpq_get_str($x, $base)
4189				: Math::GMPz::Rmpz_get_str($x, $base)
4190				);
4191				$frac .= '/1' if (index($frac, '/') == -1);
4192				return $frac;
4193				}
4194
4195				$x = _any2mpq($x) // return undef;
4196
4197				my $frac = Math::GMPq::Rmpq_get_str($x, $base);
4198				$frac .= '/1' if (index($frac, '/') == -1);
4199				$frac;
4200				}
4201
4202				sub as_dec ($;$) {
4203				my ($x, $y) = @_;
4204				require Math::AnyNum::stringify;
4205
4206				my $prec = $PREC;
4207				if (defined($y)) {
4208				if (!ref($y) and CORE::int($y) eq $y) {
4209				$prec = $y;
4210				}
4211				elsif (ref($y) eq __PACKAGE__) {
4212				$prec = _any2ui($$y) // 0;
4213				}
4214				else {
4215				$prec = _any2ui(_star2mpz($y) // return undef) // 0;
4216				}
4217
4218				$prec <<= 2;
4219
4220				state $min_prec = Math::MPFR::RMPFR_PREC_MIN();
4221				state $max_prec = Math::MPFR::RMPFR_PREC_MAX();
4222
4223				if ($prec < $min_prec or $prec > $max_prec) {
4224				require Carp;
4225				Carp::croak("precision must be between $min_prec and $max_prec, got ", $prec >> 2);
4226				}
4227				}
4228
4229				local $PREC = $prec;
4230				__stringify__(_star2mpfr_mpc($x));
4231				}
4232
4233				sub rat_approx ($) {
4234				require Math::AnyNum::stringify;
4235				my ($x) = @_;
4236
4237				$x = _star2mpfr($x);
4238
4239				Math::MPFR::Rmpfr_number_p($x) \|\| goto &nan;
4240
4241				my $t = Math::MPFR::Rmpfr_init2($PREC); # temporary variable
4242				my $r = Math::MPFR::Rmpfr_init2($PREC);
4243
4244				Math::MPFR::Rmpfr_set($r, $x, $ROUND);
4245
4246				my $num2cfrac = sub {
4247				my ($callback, $n) = @_;
4248
4249				while (1) {
4250				Math::MPFR::Rmpfr_floor($t, $r);
4251
4252				my $z = Math::GMPz::Rmpz_init();
4253				Math::MPFR::Rmpfr_get_z($z, $t, Math::MPFR::MPFR_RNDZ);
4254
4255				$callback->($z) && return 1;
4256
4257				Math::MPFR::Rmpfr_sub($r, $r, $t, $ROUND);
4258				Math::MPFR::Rmpfr_zero_p($r) && last;
4259				Math::MPFR::Rmpfr_ui_div($r, 1, $r, $ROUND);
4260				}
4261				};
4262
4263				my $q = Math::GMPq::Rmpq_init();
4264
4265				my $cfrac2num = sub {
4266				my (@f) = @_;
4267
4268				Math::GMPq::Rmpq_set_ui($q, 0, 1);
4269
4270				for (1 .. $#f) {
4271				Math::GMPq::Rmpq_add_z($q, $q, CORE::pop(@f));
4272				Math::GMPq::Rmpq_inv($q, $q);
4273				}
4274
4275				Math::GMPq::Rmpq_add_z($q, $q, $f[0]);
4276				};
4277
4278				my @cfrac;
4279				my $s = __stringify__($x);
4280				my $u = Math::MPFR::Rmpfr_init2($PREC); # temporary variable
4281
4282				#<<<
4283				$num2cfrac->(
4284				sub {
4285				my ($n) = @_;
4286				CORE::push(@cfrac, $n);
4287				$cfrac2num->(@cfrac);
4288				Math::MPFR::Rmpfr_set_q($u, $q, $ROUND);
4289				CORE::index(__stringify__($u), $s) == 0;
4290				}, $x
4291				);
4292				#>>>
4293
4294				bless \$q;
4295				}
4296
4297				sub digits ($;$) {
4298				my ($x, $y) = @_;
4299				my $str = as_int($x, $y) // return ();
4300				my @digits = split(//, $str);
4301				shift(@digits) if $digits[0] eq '-';
4302				(@digits);
4303				}
4304
4305				1; # End of Math::AnyNum